https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Doitsudoitsu&feedformat=atomAoPS Wiki - User contributions [en]2024-03-28T16:49:47ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=User:Hy2015&diff=78911User:Hy20152016-06-12T20:54:38Z<p>Doitsudoitsu: /* Miscellaneous Stuff */</p>
<hr />
<div>Hi this is my wiki page!<br />
Welcome!<br />
I'd rather you not edit my info unless it's something useful to add.<br />
You can post anything in the "Miscellaneous" section, preferably not spam.<br />
<br />
==About hy==<br />
===Username Info===<br />
I made this account back in the summer of 2015, and wasn't planning on using much. However, I really liked AoPS and became an active member of the community and all that.<br />
<br />
HY is my initials, some of you might know my name, but I'm not going to publicize my name on a wiki page.<br />
2015 came from the year I joined.<br />
<br />
Yep, pretty boring username. Still regret naming myself that. Back when I made this account, I didn't really care so that's how I came up with the most boring username ever. <br />
<br />
I am also referred to as hy, so you can call me that. <br />
<br />
===Personal Info===<br />
Name? No not telling you that.<br />
Wait why are you reading my wiki page stalker?<br />
Okay some basic info:<br />
I'm in 7th grade<br />
I'm a girl<br />
<br />
===In Real Person===<br />
Well... If you are in NY, you might meet me in NY State MC next year.<br />
<br />
==AoPS==<br />
===AoPS Resources===<br />
<math>\bullet</math>I do alcumus for Online Class homework, so I use it quite a lot.<br />
<br />
<math>\bullet</math>I go on FTW sometimes and play.<br />
<br />
<math>\bullet</math>I don't use MC Trainer a lot, but I do a few questions once in a while.<br />
<br />
<math>\bullet</math>I usually participate in Reaper games. However, I find them boring an a waste of time.<br />
My highest was 1st place, with 28th place finishing.<br />
(That was when the game just started and I was the first few to reap.)<br />
<br />
<math>\bullet</math>I play a greed control game for a couple of days, but then it gets boring.<br />
<br />
===AoPS Community===<br />
I'm a quite active member of the community. At first, I wasn't even expecting to reach 100 posts, now I have around 1400 posts. I really like AoPS and it's great.<br />
<br />
===Blog===<br />
My blog can be found [http://artofproblemsolving.com/community/c197628_a_collection_of_miscellaneous_stuff here.]<br />
However, it is private, and PM me if you want to have access to it.<br />
<br />
==Miscellaneous Stuff==<br />
is bad</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2006_AIME_II_Problems/Problem_1&diff=785952006 AIME II Problems/Problem 12016-05-18T20:56:13Z<p>Doitsudoitsu: latex</p>
<hr />
<div>== Problem ==<br />
In [[convex polygon|convex]] [[hexagon]] <math>ABCDEF</math>, all six sides are congruent, <math>\angle A</math> and <math>\angle D</math> are [[right angle]]s, and <math>\angle B, \angle C, \angle E,</math> and <math>\angle F</math> are [[congruent]]. The area of the hexagonal region is <math>2116(\sqrt{2}+1).</math> Find <math>AB</math>.<br />
<br />
== Solution ==<br />
Let the side length be called <math>x</math>, so <math>x=AB=BC=CD=DE=EF=AF</math>. <br />
<br />
[[Image:2006_II_AIME-1.png]]<br />
<br />
The diagonal <math>BF=\sqrt{AB^2+AF^2}=\sqrt{x^2+x^2}=x\sqrt{2}</math>. Then the areas of the triangles AFB and CDE in total are <math>\frac{x^2}{2}\cdot 2</math>,<br />
and the area of the rectangle BCEF equals <math>x\cdot x\sqrt{2}=x^2\sqrt{2}</math><br />
<br />
Then we have to solve the equation <br />
<div style="text-align:center;"><br />
<math>2116(\sqrt{2}+1)=x^2\sqrt{2}+x^2</math>.<br />
<br />
<math>2116(\sqrt{2}+1)=x^2(\sqrt{2}+1)</math><br />
<br />
<math>2116=x^2</math><br />
<br />
<math>x=46</math></div><br />
<br />
Therefore, <math>AB</math> is <math>\boxed{046}</math>.<br />
<br />
== Solution 2 ==<br />
<br />
Because <math>\angle<br />
B</math>, <math>\angle C</math>, <math>\angle E</math>, and <math>\angle F</math> are congruent, the degree-measure of each of them is <math><br />
{{720-2\cdot90}\over4}= 135</math>. Lines <math>BF</math> and <math>CE</math> divide the hexagonal region into two right triangles and a rectangle. Let <math>AB=x</math>. Then <math>BF=x\sqrt2</math>. Thus<br />
<math>\begin{align*}<br />
2116(\sqrt2+1)&=[ABCDEF]\\<br />
&=2\cdot {1\over2}x^2+x\cdot x\sqrt2=x^2(1+\sqrt2),<br />
\end{align*}so </math>x^2=2116<math>, and </math>x=\boxed{46}<math>.<br />
<br />
[asy]<br />
pair A,B,C,D,I,F;<br />
A=(0,0);<br />
B=(7,0);<br />
F=(0,7);<br />
I=(6,13);<br />
D=(13,13);<br />
C=(13,6);<br />
dot(A);<br />
dot(B);<br />
dot(C);<br />
dot(D);<br />
dot(I);<br />
dot(F);<br />
draw(A--B--C--D--I--F--cycle,linewidth(0.7));<br />
label("{\tiny </math>A<math>}",A,S);<br />
label("{\tiny </math>B<math>}",B,S);<br />
label("{\tiny </math>C<math>}",C,E);<br />
label("{\tiny </math>D<math>}",D,N);<br />
label("{\tiny </math>E<math>}",I,N);<br />
label("{\tiny </math>F$}",F,W);<br />
[/asy]<br />
<br />
== See also ==<br />
{{AIME box|year=2006|n=II|before=First Question|num-a=2}}<br />
<br />
[[Category:Intermediate Geometry Problems]]<br />
{{MAA Notice}}</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=78492AoPS Wiki:AoPS Community Awards2016-05-10T22:11:28Z<p>Doitsudoitsu: 2015-2016</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Shyam Narayanan (2015)<br />
* Prafulla Susil Dhariwal(2011,2012)<br />
* Akashnil Dutta(2009,2010,2011)<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009, 2011)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Bobby Shen (2012, 2013)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Victor Wang (2013)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009, 2010)<br />
* Calvin Deng (2010, 2012, 2013)<br />
* Allen Yuan (2010)<br />
* In-sung Na (2010)<br />
* Xiaoyu He (2010, 2011)<br />
* Kevin Sun (2013)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
*Jeck Lim (2012)<br />
<br />
=== Gold medalists ===<br />
* Shyam Narayanan (2015)<br />
* Akashnil Dutta(2011)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Mark Sellke (2013, 2014)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
* Xiaoyu He (2010, 2011)<br />
* Wenyu Cao (2011)<br />
* Prafulla Susil Dhariwal (2012)<br />
* Bobby Shen (2012, 2013)<br />
* James Tao (2013, 2014)<br />
* Victor Wang (2013)<br />
<br />
=== Silver medalists ===<br />
* Akashnil Dutta (2009,2010)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan (2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
* Carmela Lao (2010)<br />
* Jafar Jafarov (2006)<br />
* Ali Gurel (1996)<br />
<br />
=== Bronze medalists ===<br />
* Debdyuti Banerjee (2011)<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
* Jafar Jafarov (2007)<br />
* Kevin Sun (2013)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li (2010)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li(2010)<br />
* Eric Schneider<br />
* Kevin Zhou<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
===Gold Medalists ===<br />
* David Benjamin (2008)<br />
* Brian Hamrick (2009)<br />
* Neal Wu (2008, 2009, 2010)<br />
* Wenyu Cao (2010)<br />
* Scott Wu (2012, 2013, 2014)<br />
<br />
===Silver Medalists ===<br />
* Akashnil Dutta(2011)<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
===Bronze Medalists ===<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
* Alex Zhu (2012)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Calvin Deng (2009, 2012, 2013)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Bobby Shen (2013)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* Victor Wang (2012, 2013)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
* Evan Chen (2014)<br />
* James Tao (2014)<br />
* Scott Wu (2014)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Brian Lawrence (2008)<br />
* Mitchell Lee (2012, 2013)<br />
* Evan O'Dorney (2011, 2012, 2013)<br />
* Alexander Schwartz (2000, 2002)<br />
* Mark Sellke (2014)<br />
* Bobby Shen (2013, 2014)<br />
* Jan Siwanowicz (2001) <br />
* Arnav Tripathy (2008)<br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
* David Yang (2013, 2014)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual, 2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Jonathan Li (2011)<br />
*Evan O'Dorney (2011)<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* Matthew Babbitt (2013)<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Lewis Chen (2014)<br />
* Calvin Deng (2011)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* Shyam Narayanan (2012, 2014)<br />
* Bobby Shen (2010, 2011, 2012, 2013)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
* Alexander Whatley (2012)<br />
* Scott Wu (2012)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Lewis Chen (2014)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Daniel Li (2009)<br />
* Jonathan Li (2010)<br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009, 2011)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* Lewis Chen(2009)<br />
* Yongyi Chen (2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Michael Kural (2013)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Jonathan Li (2009, 2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Michael Ma (2009, 2010, 2011 in grades 3, 4, 5)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Shyam Narayanan (2013)<br />
* Graham O'Donnell (2015)<br />
* Edwin Peng (2013)<br />
* Max Rosett (2005, 2006) (AoPS assistant instructor)<br />
* Amrit Saxena (2009)<br />
* Eric Schneider (2009)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Lilly Shen (2009)<br />
* Richard Spence (2009)<br />
* Kyle Stankowski (2009)<br />
* Michael Tan (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* David Yang (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
=='''Perfect USAMO Index'''==<br />
*Lewis Chen (2014)<br />
*Samuel Elder (2009)<br />
*Bobby Shen (2011)<br />
*Gabriel Caroll (1998, 1999, 2000, 2001)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
* Mark Sellke (2010)<br />
* Scott Wu (2011)<br />
* Chad Qian (2012)<br />
* Alec Sun (2013)<br />
* Swapnil Garg (2014)<br />
* Kevin Liu (2015)<br />
* Edward Wan (2016)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Andrew Cai (2016)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009, 2010)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Ben Kang (2016)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* Brian Liu (2016)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Graham O'Donnell (2014)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Edward Wan (2016)<br />
* Victor Wang (2009)<br />
* Alex Wei (2016)<br />
* Eric Wei (2016)<br />
* Ben Wright (2016)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* Alex Xu (2016)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Justin Yu (2016)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
* Mark Sellke (2009, 2010)<br />
* Eugene Chen (2010)<br />
* Lewis Chen (2010)<br />
* Shyam Narayanan (2010, 2011)<br />
* Franklyn Wang (2013, 2014)<br />
*Akshaj Kadaveru (2013, 2014)<br />
*Scott Wu (2010, 2011)<br />
*Walker Kroubalkian (2015)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
* Alex Song (2010)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
* Mark Sellke (2010)<br />
*Shyam Narayanan (2011)<br />
* Kevin Liu (2014)<br />
* Andy Xu (2015)<br />
* Edward Wan (2016)<br />
<br />
=== National Team Champions ===<br />
* Team Virginia: Divya Garg, Brian Hamrick, Daniel Li, Jimmy Clark (2006)<br />
* Team Massachusetts: Alec Sun, James Lin, Michael Ren, Matthew Lipman (2013)<br />
* Team California: Swapnil Garg, Harry Wang, Rajiv Movva, Jeffery Li (2014)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
<br />
=== ARML winners ===<br />
* Alex Song (2009, 2011)<br />
* Benjamin Gunby (2010)<br />
* Allen Liu (2012, 2013)<br />
<br />
=== ARML Perfect Scorers ===<br />
* Alex Song (2011)<br />
* Shyam Narayanan (2012, 2014)<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
*Lewis Chen(2011,2012)<br />
* Benjamin Gunby (2010)<br />
* Bobby Shen (2010)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
* Alex Song (2009,2011,2012)<br />
*Bailey Wang (2009)(WOOT Grader)<br />
* Shyam Narayanan (2011, 2012 (Perfect Score), 2014 (Perfect Score), 2015)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=78491AoPS Wiki:AoPS Community Awards2016-05-10T22:08:41Z<p>Doitsudoitsu: not sure about alex wei</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Shyam Narayanan (2015)<br />
* Prafulla Susil Dhariwal(2011,2012)<br />
* Akashnil Dutta(2009,2010,2011)<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009, 2011)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Bobby Shen (2012, 2013)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Victor Wang (2013)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009, 2010)<br />
* Calvin Deng (2010, 2012, 2013)<br />
* Allen Yuan (2010)<br />
* In-sung Na (2010)<br />
* Xiaoyu He (2010, 2011)<br />
* Kevin Sun (2013)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
*Jeck Lim (2012)<br />
<br />
=== Gold medalists ===<br />
* Shyam Narayanan (2015)<br />
* Akashnil Dutta(2011)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Mark Sellke (2013, 2014)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
* Xiaoyu He (2010, 2011)<br />
* Wenyu Cao (2011)<br />
* Prafulla Susil Dhariwal (2012)<br />
* Bobby Shen (2012, 2013)<br />
* James Tao (2013, 2014)<br />
* Victor Wang (2013)<br />
<br />
=== Silver medalists ===<br />
* Akashnil Dutta (2009,2010)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan (2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
* Carmela Lao (2010)<br />
* Jafar Jafarov (2006)<br />
* Ali Gurel (1996)<br />
<br />
=== Bronze medalists ===<br />
* Debdyuti Banerjee (2011)<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
* Jafar Jafarov (2007)<br />
* Kevin Sun (2013)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li (2010)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li(2010)<br />
* Eric Schneider<br />
* Kevin Zhou<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
===Gold Medalists ===<br />
* David Benjamin (2008)<br />
* Brian Hamrick (2009)<br />
* Neal Wu (2008, 2009, 2010)<br />
* Wenyu Cao (2010)<br />
* Scott Wu (2012, 2013, 2014)<br />
<br />
===Silver Medalists ===<br />
* Akashnil Dutta(2011)<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
===Bronze Medalists ===<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
* Alex Zhu (2012)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Calvin Deng (2009, 2012, 2013)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Bobby Shen (2013)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* Victor Wang (2012, 2013)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
* Evan Chen (2014)<br />
* James Tao (2014)<br />
* Scott Wu (2014)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Brian Lawrence (2008)<br />
* Mitchell Lee (2012, 2013)<br />
* Evan O'Dorney (2011, 2012, 2013)<br />
* Alexander Schwartz (2000, 2002)<br />
* Mark Sellke (2014)<br />
* Bobby Shen (2013, 2014)<br />
* Jan Siwanowicz (2001) <br />
* Arnav Tripathy (2008)<br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
* David Yang (2013, 2014)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual, 2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Jonathan Li (2011)<br />
*Evan O'Dorney (2011)<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* Matthew Babbitt (2013)<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Lewis Chen (2014)<br />
* Calvin Deng (2011)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* Shyam Narayanan (2012, 2014)<br />
* Bobby Shen (2010, 2011, 2012, 2013)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
* Alexander Whatley (2012)<br />
* Scott Wu (2012)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Lewis Chen (2014)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Daniel Li (2009)<br />
* Jonathan Li (2010)<br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009, 2011)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* Lewis Chen(2009)<br />
* Yongyi Chen (2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Michael Kural (2013)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Jonathan Li (2009, 2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Michael Ma (2009, 2010, 2011 in grades 3, 4, 5)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Shyam Narayanan (2013)<br />
* Graham O'Donnell (2015)<br />
* Edwin Peng (2013)<br />
* Max Rosett (2005, 2006) (AoPS assistant instructor)<br />
* Amrit Saxena (2009)<br />
* Eric Schneider (2009)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Lilly Shen (2009)<br />
* Richard Spence (2009)<br />
* Kyle Stankowski (2009)<br />
* Michael Tan (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* David Yang (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
=='''Perfect USAMO Index'''==<br />
*Lewis Chen (2014)<br />
*Samuel Elder (2009)<br />
*Bobby Shen (2011)<br />
*Gabriel Caroll (1998, 1999, 2000, 2001)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
* Mark Sellke (2010)<br />
* Scott Wu (2011)<br />
* Chad Qian (2012)<br />
* Alec Sun (2013)<br />
* Swapnil Garg (2014)<br />
* Kevin Liu (2015)<br />
* Edward Wan (2016)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Andrew Cai (2016)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009, 2010)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Ben Kang (2016)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* Brian Liu (2016)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Graham O'Donnell (2014)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Edward Wan (2016)<br />
* Victor Wang (2009)<br />
* Alex Wei (2016)<br />
* Eric Wei (2016)<br />
* Ben Wright (2016)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* Alex Xu (2016)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Justin Yu (2016)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
* Mark Sellke (2009, 2010)<br />
* Eugene Chen (2010)<br />
* Lewis Chen (2010)<br />
* Shyam Narayanan (2010, 2011)<br />
* Franklyn Wang (2013, 2014)<br />
*Akshaj Kadaveru (2013, 2014)<br />
*Scott Wu (2010, 2011)<br />
*Walker Kroubalkian (2015)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
* Alex Song (2010)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
* Mark Sellke (2010)<br />
*Shyam Narayanan (2011)<br />
* Kevin Liu (2014)<br />
<br />
=== National Team Champions ===<br />
* Team Virginia: Divya Garg, Brian Hamrick, Daniel Li, Jimmy Clark (2006)<br />
* Team Massachusetts: Alec Sun, James Lin, Michael Ren, Matthew Lipman (2013)<br />
* Team California: Swapnil Garg, Harry Wang, Rajiv Movva, Jeffery Li (2014)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
<br />
=== ARML winners ===<br />
* Alex Song (2009, 2011)<br />
* Benjamin Gunby (2010)<br />
* Allen Liu (2012, 2013)<br />
<br />
=== ARML Perfect Scorers ===<br />
* Alex Song (2011)<br />
* Shyam Narayanan (2012, 2014)<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
*Lewis Chen(2011,2012)<br />
* Benjamin Gunby (2010)<br />
* Bobby Shen (2010)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
* Alex Song (2009,2011,2012)<br />
*Bailey Wang (2009)(WOOT Grader)<br />
* Shyam Narayanan (2011, 2012 (Perfect Score), 2014 (Perfect Score), 2015)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=78490AoPS Wiki:AoPS Community Awards2016-05-10T22:02:41Z<p>Doitsudoitsu: edward wan has an aops that i should not reveal without his consent</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Shyam Narayanan (2015)<br />
* Prafulla Susil Dhariwal(2011,2012)<br />
* Akashnil Dutta(2009,2010,2011)<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009, 2011)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Bobby Shen (2012, 2013)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Victor Wang (2013)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009, 2010)<br />
* Calvin Deng (2010, 2012, 2013)<br />
* Allen Yuan (2010)<br />
* In-sung Na (2010)<br />
* Xiaoyu He (2010, 2011)<br />
* Kevin Sun (2013)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
*Jeck Lim (2012)<br />
<br />
=== Gold medalists ===<br />
* Shyam Narayanan (2015)<br />
* Akashnil Dutta(2011)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Mark Sellke (2013, 2014)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
* Xiaoyu He (2010, 2011)<br />
* Wenyu Cao (2011)<br />
* Prafulla Susil Dhariwal (2012)<br />
* Bobby Shen (2012, 2013)<br />
* James Tao (2013, 2014)<br />
* Victor Wang (2013)<br />
<br />
=== Silver medalists ===<br />
* Akashnil Dutta (2009,2010)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan (2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
* Carmela Lao (2010)<br />
* Jafar Jafarov (2006)<br />
* Ali Gurel (1996)<br />
<br />
=== Bronze medalists ===<br />
* Debdyuti Banerjee (2011)<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
* Jafar Jafarov (2007)<br />
* Kevin Sun (2013)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li (2010)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li(2010)<br />
* Eric Schneider<br />
* Kevin Zhou<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
===Gold Medalists ===<br />
* David Benjamin (2008)<br />
* Brian Hamrick (2009)<br />
* Neal Wu (2008, 2009, 2010)<br />
* Wenyu Cao (2010)<br />
* Scott Wu (2012, 2013, 2014)<br />
<br />
===Silver Medalists ===<br />
* Akashnil Dutta(2011)<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
===Bronze Medalists ===<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
* Alex Zhu (2012)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Calvin Deng (2009, 2012, 2013)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Bobby Shen (2013)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* Victor Wang (2012, 2013)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
* Evan Chen (2014)<br />
* James Tao (2014)<br />
* Scott Wu (2014)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Brian Lawrence (2008)<br />
* Mitchell Lee (2012, 2013)<br />
* Evan O'Dorney (2011, 2012, 2013)<br />
* Alexander Schwartz (2000, 2002)<br />
* Mark Sellke (2014)<br />
* Bobby Shen (2013, 2014)<br />
* Jan Siwanowicz (2001) <br />
* Arnav Tripathy (2008)<br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
* David Yang (2013, 2014)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual, 2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Jonathan Li (2011)<br />
*Evan O'Dorney (2011)<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* Matthew Babbitt (2013)<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Lewis Chen (2014)<br />
* Calvin Deng (2011)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* Shyam Narayanan (2012, 2014)<br />
* Bobby Shen (2010, 2011, 2012, 2013)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
* Alexander Whatley (2012)<br />
* Scott Wu (2012)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Lewis Chen (2014)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Daniel Li (2009)<br />
* Jonathan Li (2010)<br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009, 2011)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* Lewis Chen(2009)<br />
* Yongyi Chen (2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Michael Kural (2013)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Jonathan Li (2009, 2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Michael Ma (2009, 2010, 2011 in grades 3, 4, 5)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Shyam Narayanan (2013)<br />
* Graham O'Donnell (2015)<br />
* Edwin Peng (2013)<br />
* Max Rosett (2005, 2006) (AoPS assistant instructor)<br />
* Amrit Saxena (2009)<br />
* Eric Schneider (2009)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Lilly Shen (2009)<br />
* Richard Spence (2009)<br />
* Kyle Stankowski (2009)<br />
* Michael Tan (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* David Yang (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
=='''Perfect USAMO Index'''==<br />
*Lewis Chen (2014)<br />
*Samuel Elder (2009)<br />
*Bobby Shen (2011)<br />
*Gabriel Caroll (1998, 1999, 2000, 2001)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
* Mark Sellke (2010)<br />
* Scott Wu (2011)<br />
* Chad Qian (2012)<br />
* Alec Sun (2013)<br />
* Swapnil Garg (2014)<br />
* Kevin Liu (2015)<br />
* Edward Wan (2016)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009, 2010)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Graham O'Donnell (2014)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Victor Wang (2009)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
* Mark Sellke (2009, 2010)<br />
* Eugene Chen (2010)<br />
* Lewis Chen (2010)<br />
* Shyam Narayanan (2010, 2011)<br />
* Franklyn Wang (2013, 2014)<br />
*Akshaj Kadaveru (2013, 2014)<br />
*Scott Wu (2010, 2011)<br />
*Walker Kroubalkian (2015)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
* Alex Song (2010)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
* Mark Sellke (2010)<br />
*Shyam Narayanan (2011)<br />
* Kevin Liu (2014)<br />
<br />
=== National Team Champions ===<br />
* Team Virginia: Divya Garg, Brian Hamrick, Daniel Li, Jimmy Clark (2006)<br />
* Team Massachusetts: Alec Sun, James Lin, Michael Ren, Matthew Lipman (2013)<br />
* Team California: Swapnil Garg, Harry Wang, Rajiv Movva, Jeffery Li (2014)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
<br />
=== ARML winners ===<br />
* Alex Song (2009, 2011)<br />
* Benjamin Gunby (2010)<br />
* Allen Liu (2012, 2013)<br />
<br />
=== ARML Perfect Scorers ===<br />
* Alex Song (2011)<br />
* Shyam Narayanan (2012, 2014)<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
*Lewis Chen(2011,2012)<br />
* Benjamin Gunby (2010)<br />
* Bobby Shen (2010)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
* Alex Song (2009,2011,2012)<br />
*Bailey Wang (2009)(WOOT Grader)<br />
* Shyam Narayanan (2011, 2012 (Perfect Score), 2014 (Perfect Score), 2015)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=78489User:Phi ftw16182016-05-10T22:00:46Z<p>Doitsudoitsu: /* Vandalism Space */</p>
<hr />
<div>Apparently I get a user page! Fun!<br />
<br />
==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
<br />
The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
<br />
Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
<br />
The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
<br />
In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
<br />
===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
<br />
===Phi IRL===<br />
Phi is going to AwesomeMath 2016 at Puget Sound. He has made MATHCOUNTS State twice, but as for his competition results... haha, that's a nice joke. There aren't any notable ones.<br />
<br />
==AoPS Resource Usage==<br />
===FTW===<br />
Phi does play FTW occasionally, although when he does, it usually does not go well. His rating is around 1400, although that may change because after his MATHCOUNTS career, he will probably end up getting worse at speed mathematics. Compared to other AoPSers who are considered to be 'pro', phi_ftw1618 looks like a very bad FTW competitor.<br />
===Alcumus===<br />
phi_ftw1618 played a lot of Alcumus in preparation for his MATHCOUNTS and AMC 8 competitions. He eventually ended up mastering every topic, but does not use Alcumus very much right now except in last-minute preparation for some contests. He also does use Alcumus when he's bored at school, which happens surprisingly often.<br />
===MATHCOUNTS Trainer===<br />
phi_ftw1618 barely used MATHCOUNTS trainer except for getting school and chapter-level problems nailed because he prefers the Alcumus approach. He does have access to all 4 levels of problems, but still prefers Alcumus.<br />
===Reaper===<br />
phi_ftw1618 has tried numerous times to do well in Reaper, but has failed every time, with his best finish being a 9th place. He now thinks that Reaper is a waste of time unless the time between reaps is an hour or less, as otherwise, a reap becomes too valuable.<br />
===Greed Control===<br />
phi_ftw1618 is surprisingly bad at consistently inputting (relatively) small integers into a computer. Thus, he is quite bad at Greed Control as well. This is quite unfortunate, as it's easier on his sleep schedule to do well on Greed Control than Reaper.<br />
<br />
==Community==<br />
===Forums===<br />
phi_ftw1618 is on the forums a lot, possibly more than he should be. He usually uses the forums for both math and as a message board. Moreover, he also spends (probably too much) time with pandabear10 in various locations. He also plays on the Games forums, although currently makes it a rule of thumb to never post on either the Fun Factory or Frivolous Forum. He somehow has amassed 1183 posts despite not having more than 400 posts in any post-counting forum. <br />
===Blog===<br />
phi_ftw1618 runs a blog which is known mostly as [http://artofproblemsolving.com/community/c74051 the Phi Blog]. While it started as "a dumping ground for philosophy nonsense", it became a place for him to post anything and everything on a daily basis. It is now currently one of the few blogs on the blogroll that update daily (with three contributors for backup) and usually more often on days when he feels like it. The blog is used for everything that he needs, that is, he only owns the one blog, plus a forgotten one that is more public, but rarely used.<br />
<br />
The CSS for the blog was designed by NeoMathematicalKid, and is the result of phi_ftw1618 spending too much time looking at NMK's github for AoPS blogs.<br />
<br />
The blog was originally created 5/5/15, and currently has over 6000 views, 500+ comments, and 100+ shouts, which was the result of an unfortunate CSS accident that was later resolved, but still is quite buggy. He intends to repair this when he has time. However, he doesn't usually have time.<br />
<br />
==Trivia==<br />
<br />
*Phi also participates in Science Olympiad.<br />
*He has met pandabear10, Xinyan, and goseahawks in real life.<br />
*Phi sometimes refers to himself as phi IRL (why?).<br />
*Strangely enough, he has never taken an AoPS Online Class.<br />
*He also pronounces AoPS like "ay-ops" not "Ay-oh-pee-ess".<br />
*Phi speaks French.<br />
*Phi has run out of random facts to give you.<br />
<br />
==Crowdsourced Section==<br />
<br />
haha funny as if anyone will ever read this<br />
If you want to get a post into this section (short comment or so) post on my blog. I think I put something there (might be wrong).<br />
<br />
==Vandalism Space==<br />
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v</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=78120User:Phi ftw16182016-04-18T20:35:51Z<p>Doitsudoitsu: /* Vandalism Space */</p>
<hr />
<div>Apparently I get a user page! Fun!<br />
<br />
==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
<br />
The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
<br />
Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
<br />
The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
<br />
In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
<br />
===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
<br />
===Phi IRL===<br />
Phi is going to AwesomeMath 2016 at Puget Sound. He has made MATHCOUNTS State twice, but as for his competition results... haha, that's a nice joke. There aren't any notable ones.<br />
<br />
==AoPS Resource Usage==<br />
===FTW===<br />
Phi does play FTW occasionally, although when he does, it usually does not go well. His rating is around 1400, although that may change because after his MATHCOUNTS career, he will probably end up getting worse at speed mathematics. Compared to other AoPSers who are considered to be 'pro', phi_ftw1618 looks like a very bad FTW competitor.<br />
===Alcumus===<br />
phi_ftw1618 played a lot of Alcumus in preparation for his MATHCOUNTS and AMC 8 competitions. He eventually ended up mastering every topic, but does not use Alcumus very much right now except in last-minute preparation for some contests. He also does use Alcumus when he's bored at school, which happens surprisingly often.<br />
===MATHCOUNTS Trainer===<br />
phi_ftw1618 barely used MATHCOUNTS trainer except for getting school and chapter-level problems nailed because he prefers the Alcumus approach. He does have access to all 4 levels of problems, but still prefers Alcumus.<br />
===Reaper===<br />
phi_ftw1618 has tried numerous times to do well in Reaper, but has failed every time, with his best finish being a 9th place. He now thinks that Reaper is a waste of time unless the time between reaps is an hour or less, as otherwise, a reap becomes too valuable.<br />
===Greed Control===<br />
phi_ftw1618 is surprisingly bad at consistently inputting (relatively) small integers into a computer. Thus, he is quite bad at Greed Control as well. This is quite unfortunate, as it's easier on his sleep schedule to do well on Greed Control than Reaper.<br />
<br />
==Community==<br />
===Forums===<br />
phi_ftw1618 is on the forums a lot, possibly more than he should be. He usually uses the forums for both math and as a message board. Moreover, he also spends (probably too much) time with pandabear10 in various locations. He also plays on the Games forums, although currently makes it a rule of thumb to never post on either the Fun Factory or Frivolous Forum. He somehow has amassed 1183 posts despite not having more than 400 posts in any post-counting forum. <br />
===Blog===<br />
phi_ftw1618 runs a blog which is known mostly as [http://artofproblemsolving.com/community/c74051 the Phi Blog]. While it started as "a dumping ground for philosophy nonsense", it became a place for him to post anything and everything on a daily basis. It is now currently one of the few blogs on the blogroll that update daily (with three contributors for backup) and usually more often on days when he feels like it. The blog is used for everything that he needs, that is, he only owns the one blog, plus a forgotten one that is more public, but rarely used.<br />
<br />
The CSS for the blog was designed by NeoMathematicalKid, and is the result of phi_ftw1618 spending too much time looking at NMK's github for AoPS blogs.<br />
<br />
The blog was originally created 5/5/15, and currently has over 6000 views, 500+ comments, and 100+ shouts, which was the result of an unfortunate CSS accident that was later resolved, but still is quite buggy. He intends to repair this when he has time. However, he doesn't usually have time.<br />
<br />
==Trivia==<br />
<br />
*Phi also participates in Science Olympiad.<br />
*He has met pandabear10, Xinyan, and goseahawks in real life.<br />
*Phi sometimes refers to himself as phi IRL.<br />
*Strangely enough, he has never taken an AoPS Online Class.<br />
*He also pronounces AoPS like "ay-ops" not "Ay-oh-pee-ess".<br />
*Phi speaks French.<br />
*Phi has run out of random facts to give you.<br />
<br />
==Crowdsourced Section==<br />
<br />
haha funny as if anyone will ever read this<br />
If you want to get a post into this section (short comment or so) post on my blog. I think I put something there (might be wrong).<br />
<br />
==Vandalism Space==<br />
rly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly 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inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly inrly in</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=78002User:Phi ftw16182016-04-10T21:05:00Z<p>Doitsudoitsu: /* Vandalism Space */</p>
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<div>Apparently I get a user page! Fun!<br />
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==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
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The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
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Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
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The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
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In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
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===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
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===Phi IRL===<br />
Phi is going to AwesomeMath 2016 at Puget Sound. He has made MATHCOUNTS State twice, but as for his competition results... haha, that's a nice joke. There aren't any notable ones.<br />
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==AoPS Resource Usage==<br />
===FTW===<br />
Phi does play FTW occasionally, although when he does, it usually does not go well. His rating is around 1400, although that may change because after his MATHCOUNTS career, he will probably end up getting worse at speed mathematics. Compared to other AoPSers who are considered to be 'pro', phi_ftw1618 looks like a very bad FTW competitor.<br />
===Alcumus===<br />
phi_ftw1618 played a lot of Alcumus in preparation for his MATHCOUNTS and AMC 8 competitions. He eventually ended up mastering every topic, but does not use Alcumus very much right now except in last-minute preparation for some contests. He also does use Alcumus when he's bored at school, which happens surprisingly often.<br />
===MATHCOUNTS Trainer===<br />
phi_ftw1618 barely used MATHCOUNTS trainer except for getting school and chapter-level problems nailed because he prefers the Alcumus approach. He does have access to all 4 levels of problems, but still prefers Alcumus.<br />
===Reaper===<br />
phi_ftw1618 has tried numerous times to do well in Reaper, but has failed every time, with his best finish being a 9th place. He now thinks that Reaper is a waste of time unless the time between reaps is an hour or less, as otherwise, a reap becomes too valuable.<br />
===Greed Control===<br />
phi_ftw1618 is surprisingly bad at consistently inputting (relatively) small integers into a computer. Thus, he is quite bad at Greed Control as well. This is quite unfortunate, as it's easier on his sleep schedule to do well on Greed Control than Reaper.<br />
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==Community==<br />
===Forums===<br />
phi_ftw1618 is on the forums a lot, possibly more than he should be. He usually uses the forums for both math and as a message board. Moreover, he also spends (probably too much) time with pandabear10 in various locations. He also plays on the Games forums, although currently makes it a rule of thumb to never post on either the Fun Factory or Frivolous Forum. He somehow has amassed 1183 posts despite not having more than 400 posts in any post-counting forum. <br />
===Blog===<br />
phi_ftw1618 runs a blog which is known mostly as [http://artofproblemsolving.com/community/c74051 the Phi Blog]. While it started as "a dumping ground for philosophy nonsense", it became a place for him to post anything and everything on a daily basis. It is now currently one of the few blogs on the blogroll that update daily (with three contributors for backup) and usually more often on days when he feels like it. The blog is used for everything that he needs, that is, he only owns the one blog, plus a forgotten one that is more public, but rarely used.<br />
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The CSS for the blog was designed by NeoMathematicalKid, and is the result of phi_ftw1618 spending too much time looking at NMK's github for AoPS blogs.<br />
<br />
The blog was originally created 5/5/15, and currently has over 6000 views, 500+ comments, and 100+ shouts, which was the result of an unfortunate CSS accident that was later resolved, but still is quite buggy. He intends to repair this when he has time. However, he doesn't usually have time.<br />
<br />
==Trivia==<br />
<br />
*Phi also participates in Science Olympiad.<br />
*He has met pandabear10, Xinyan, and goseahawks in real life.<br />
*Phi sometimes refers to himself as phi IRL.<br />
*Strangely enough, he has never taken an AoPS Online Class.<br />
*He also pronounces AoPS like "ay-ops" not "Ay-oh-pee-ess".<br />
*Phi speaks French.<br />
*Phi has run out of random facts to give you.<br />
<br />
==Crowdsourced Section==<br />
<br />
haha funny as if anyone will ever read this<br />
If you want to get a post into this section (short comment or so) post on my blog. I think I put something there (might be wrong).<br />
<br />
==Vandalism Space==<br />
jjgpksdljdof;ljv;sdlff</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=78001User:Phi ftw16182016-04-10T21:04:45Z<p>Doitsudoitsu: /* Vandalism Space */</p>
<hr />
<div>Apparently I get a user page! Fun!<br />
<br />
==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
<br />
The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
<br />
Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
<br />
The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
<br />
In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
<br />
===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
<br />
===Phi IRL===<br />
Phi is going to AwesomeMath 2016 at Puget Sound. He has made MATHCOUNTS State twice, but as for his competition results... haha, that's a nice joke. There aren't any notable ones.<br />
<br />
==AoPS Resource Usage==<br />
===FTW===<br />
Phi does play FTW occasionally, although when he does, it usually does not go well. His rating is around 1400, although that may change because after his MATHCOUNTS career, he will probably end up getting worse at speed mathematics. Compared to other AoPSers who are considered to be 'pro', phi_ftw1618 looks like a very bad FTW competitor.<br />
===Alcumus===<br />
phi_ftw1618 played a lot of Alcumus in preparation for his MATHCOUNTS and AMC 8 competitions. He eventually ended up mastering every topic, but does not use Alcumus very much right now except in last-minute preparation for some contests. He also does use Alcumus when he's bored at school, which happens surprisingly often.<br />
===MATHCOUNTS Trainer===<br />
phi_ftw1618 barely used MATHCOUNTS trainer except for getting school and chapter-level problems nailed because he prefers the Alcumus approach. He does have access to all 4 levels of problems, but still prefers Alcumus.<br />
===Reaper===<br />
phi_ftw1618 has tried numerous times to do well in Reaper, but has failed every time, with his best finish being a 9th place. He now thinks that Reaper is a waste of time unless the time between reaps is an hour or less, as otherwise, a reap becomes too valuable.<br />
===Greed Control===<br />
phi_ftw1618 is surprisingly bad at consistently inputting (relatively) small integers into a computer. Thus, he is quite bad at Greed Control as well. This is quite unfortunate, as it's easier on his sleep schedule to do well on Greed Control than Reaper.<br />
<br />
==Community==<br />
===Forums===<br />
phi_ftw1618 is on the forums a lot, possibly more than he should be. He usually uses the forums for both math and as a message board. Moreover, he also spends (probably too much) time with pandabear10 in various locations. He also plays on the Games forums, although currently makes it a rule of thumb to never post on either the Fun Factory or Frivolous Forum. He somehow has amassed 1183 posts despite not having more than 400 posts in any post-counting forum. <br />
===Blog===<br />
phi_ftw1618 runs a blog which is known mostly as [http://artofproblemsolving.com/community/c74051 the Phi Blog]. While it started as "a dumping ground for philosophy nonsense", it became a place for him to post anything and everything on a daily basis. It is now currently one of the few blogs on the blogroll that update daily (with three contributors for backup) and usually more often on days when he feels like it. The blog is used for everything that he needs, that is, he only owns the one blog, plus a forgotten one that is more public, but rarely used.<br />
<br />
The CSS for the blog was designed by NeoMathematicalKid, and is the result of phi_ftw1618 spending too much time looking at NMK's github for AoPS blogs.<br />
<br />
The blog was originally created 5/5/15, and currently has over 6000 views, 500+ comments, and 100+ shouts, which was the result of an unfortunate CSS accident that was later resolved, but still is quite buggy. He intends to repair this when he has time. However, he doesn't usually have time.<br />
<br />
==Trivia==<br />
<br />
*Phi also participates in Science Olympiad.<br />
*He has met pandabear10, Xinyan, and goseahawks in real life.<br />
*Phi sometimes refers to himself as phi IRL.<br />
*Strangely enough, he has never taken an AoPS Online Class.<br />
*He also pronounces AoPS like "ay-ops" not "Ay-oh-pee-ess".<br />
*Phi speaks French.<br />
*Phi has run out of random facts to give you.<br />
<br />
==Crowdsourced Section==<br />
<br />
haha funny as if anyone will ever read this<br />
If you want to get a post into this section (short comment or so) post on my blog. I think I put something there (might be wrong).<br />
<br />
==Vandalism Space==<br />
[img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img][img]http://gfxlovers.com/smilies/imgs/film/film015_2.gif[/img]v</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=77787AoPS Wiki:AoPS Community Awards2016-03-22T19:00:54Z<p>Doitsudoitsu: walker tesla</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Shyam Narayanan (2015)<br />
* Prafulla Susil Dhariwal(2011,2012)<br />
* Akashnil Dutta(2009,2010,2011)<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009, 2011)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Bobby Shen (2012, 2013)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Victor Wang (2013)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009, 2010)<br />
* Calvin Deng (2010, 2012, 2013)<br />
* Allen Yuan (2010)<br />
* In-sung Na (2010)<br />
* Xiaoyu He (2010, 2011)<br />
* Kevin Sun (2013)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
*Jeck Lim (2012)<br />
<br />
=== Gold medalists ===<br />
* Shyam Narayanan (2015)<br />
* Akashnil Dutta(2011)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Mark Sellke (2013, 2014)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
* Xiaoyu He (2010, 2011)<br />
* Wenyu Cao (2011)<br />
* Prafulla Susil Dhariwal (2012)<br />
* Bobby Shen (2012, 2013)<br />
* James Tao (2013, 2014)<br />
* Victor Wang (2013)<br />
<br />
=== Silver medalists ===<br />
* Akashnil Dutta (2009,2010)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan (2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
* Carmela Lao (2010)<br />
* Jafar Jafarov (2006)<br />
* Ali Gurel (1996)<br />
<br />
=== Bronze medalists ===<br />
* Debdyuti Banerjee (2011)<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
* Jafar Jafarov (2007)<br />
* Kevin Sun (2013)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li (2010)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
* Daniel Li(2010)<br />
* Eric Schneider<br />
* Kevin Zhou<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
===Gold Medalists ===<br />
* David Benjamin (2008)<br />
* Brian Hamrick (2009)<br />
* Neal Wu (2008, 2009, 2010)<br />
* Wenyu Cao (2010)<br />
* Scott Wu (2012, 2013, 2014)<br />
<br />
===Silver Medalists ===<br />
* Akashnil Dutta(2011)<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
===Bronze Medalists ===<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
* Alex Zhu (2012)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Calvin Deng (2009, 2012, 2013)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Bobby Shen (2013)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* Victor Wang (2012, 2013)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
* Evan Chen (2014)<br />
* James Tao (2014)<br />
* Scott Wu (2014)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Brian Lawrence (2008)<br />
* Mitchell Lee (2012, 2013)<br />
* Evan O'Dorney (2011, 2012, 2013)<br />
* Alexander Schwartz (2000, 2002)<br />
* Mark Sellke (2014)<br />
* Bobby Shen (2013, 2014)<br />
* Jan Siwanowicz (2001) <br />
* Arnav Tripathy (2008)<br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
* David Yang (2013, 2014)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual, 2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Jonathan Li (2011)<br />
*Evan O'Dorney (2011)<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* Matthew Babbitt (2013)<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Lewis Chen (2014)<br />
* Calvin Deng (2011)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* Shyam Narayanan (2012, 2014)<br />
* Bobby Shen (2010, 2011, 2012, 2013)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
* Alexander Whatley (2012)<br />
* Scott Wu (2012)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Lewis Chen (2014)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Daniel Li (2009)<br />
* Jonathan Li (2010)<br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Shyam Narayanan (2015)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009, 2011)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* Lewis Chen(2009)<br />
* Yongyi Chen (2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Michael Kural (2013)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Jonathan Li (2009, 2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Michael Ma (2009, 2010, 2011 in grades 3, 4, 5)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Shyam Narayanan (2013)<br />
* Graham O'Donnell (2015)<br />
* Edwin Peng (2013)<br />
* Max Rosett (2005, 2006) (AoPS assistant instructor)<br />
* Amrit Saxena (2009)<br />
* Eric Schneider (2009)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Lilly Shen (2009)<br />
* Richard Spence (2009)<br />
* Kyle Stankowski (2009)<br />
* Michael Tan (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* David Yang (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
=='''Perfect USAMO Index'''==<br />
*Lewis Chen (2014)<br />
*Samuel Elder (2009)<br />
*Bobby Shen (2011)<br />
*Gabriel Caroll (1998, 1999, 2000, 2001)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
* Mark Sellke (2010)<br />
* Scott Wu (2011)<br />
* Chad Qian (2012)<br />
* Alec Sun (2013)<br />
* Swapnil Garg (2014)<br />
* Kevin Liu (2015)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009, 2010)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Graham O'Donnell (2014)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Victor Wang (2009)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
* Mark Sellke (2009, 2010)<br />
* Eugene Chen (2010)<br />
* Lewis Chen (2010)<br />
* Shyam Narayanan (2010, 2011)<br />
* Franklyn Wang (2013, 2014)<br />
*Akshaj Kadaveru (2013, 2014)<br />
*Scott Wu (2010, 2011)<br />
*Walker Kroubalkian (2015)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
* Alex Song (2010)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
* Mark Sellke (2010)<br />
*Shyam Narayanan (2011)<br />
* Kevin Liu (2014)<br />
<br />
=== National Team Champions ===<br />
* Team Virginia: Divya Garg, Brian Hamrick, Daniel Li, Jimmy Clark (2006)<br />
* Team Massachusetts: Alec Sun, James Lin, Michael Ren, Matthew Lipman (2013)<br />
* Team California: Swapnil Garg, Harry Wang, Rajiv Movva, Jeffery Li (2014)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
<br />
=== ARML winners ===<br />
* Alex Song (2009, 2011)<br />
* Benjamin Gunby (2010)<br />
* Allen Liu (2012, 2013)<br />
<br />
=== ARML Perfect Scorers ===<br />
* Alex Song (2011)<br />
* Shyam Narayanan (2012, 2014)<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
*Lewis Chen(2011,2012)<br />
* Benjamin Gunby (2010)<br />
* Bobby Shen (2010)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
* Alex Song (2009,2011,2012)<br />
*Bailey Wang (2009)(WOOT Grader)<br />
* Shyam Narayanan (2011, 2012 (Perfect Score), 2014 (Perfect Score), 2015)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=Phi&diff=77727Phi2016-03-21T03:52:59Z<p>Doitsudoitsu: fwerweqrcqeq</p>
<hr />
<div>'''Phi''' (in lowercase, either <math>\phi</math> or <math>\varphi</math>; capitalized, <math>\Phi</math>) is the 21st letter in the Greek alphabet. It is used frequently in mathematical writing, often to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>. (The Greek letter [[Tau]] (<math>\tau</math>) was also used for this purpose in pre-Renaissance times.)<br />
<br />
==Use==<br />
<math>\phi</math> appears in a variety of different mathematical contexts: it is the limit of the ratio of successive terms of the [[Fibonacci sequence]], as well as the positive solution of the [[quadratic equation]] <math>x^2-x-1=0</math>.<br />
<br />
<math>\phi</math> is also equal to the [[continued fraction]] <math>1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\cdots}}}}</math> and the [[nested radical|continued radical]] <math>\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}</math>. It is the only positive real number that is one more than its [[multiplicative inverse]] and one less than its [[reciprocal]].<br />
<br />
It is also <math>{\lim_{x \to \infty}} \frac{F_{x+1}}{F_x}</math> where <math>F_n</math> is the nth number in the [[Fibonacci sequence]]. In other words, if you divide the n<sup>th</sup> term of the Fibonacci series over the (n-1)<sup>th</sup> term, the result approaches <math>\phi</math> as n increases.<br />
<br />
==Golden ratio==<br />
<math>\phi</math> is also known as the Golden Ratio. It was commonly believed by the Greeks to be the most aesthetically pleasing ratio between side lengths in a [[rectangle]]. The [[Golden Rectangle]] is a rectangle with side lengths of 1 and <math>\phi</math>; it has a number of interesting properties.<br />
<br />
The first fifteen digits of <math>\phi</math> in decimal representation are <math>1.61803398874989</math><br />
<br />
==Other Usages==<br />
* <math>\phi</math> is also commonly used to represent [[Euler's totient function]].<br />
<br />
==See also==<br />
* [[Irrational number]]<br />
* [[Geometry]]<br />
* [[Zeckendorf representation]]<br />
<br />
[[Category:Constants]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=Oklahoma_MathCounts&diff=77619Oklahoma MathCounts2016-03-17T00:43:58Z<p>Doitsudoitsu: salty57</p>
<hr />
<div>==Regional Competition==<br />
<br />
Oklahoma calls chapter competition as regionals. There are five distinct regions. Each region competes on a certain date.<br />
*Central: first weekend of February or last weekend of January<br />
*East central: one week after central<br />
*Eastern: two weeks after central<br />
*Northwestern: three weeks after central<br />
*Southwestern: four weeks after central<br />
<br />
Eastern region has been eliminated in 2015. It is uncertain about their existence in the future.<br />
<br />
The most competitive of these five regions are the ones with Oklahoma's two major metropolis: east central (Tulsa) and central (Oklahoma City/Norman).<br />
<br />
The selection process for advancing towards state competition is the same as all states. Countdown round is not used to determine state qualification.<br />
<br />
==State Competition==<br />
<br />
State competition is usually held on the first weekend of March. Approximately <math>80-88</math> students compete each year. Countdown round is official.<br />
<br />
===Past State Competition Winners===<br />
<br />
*2016: Vincent Li<br />
*2015: Vincent Li (Whittier Middle School)<br />
*2014: George Wang (Jenks Middle School)<br />
*2013: Amber Bick (Jenks Middle School)<br />
*2012: Thatcher Chonka (Metro Christian Academy)<br />
<br />
===Past State Competition Team Winners===<br />
<br />
*2016: Whittier Middle School<br />
*2015: Whittier Middle School<br />
*2014: Whittier Middle School<br />
*2013: Jenks Middle School<br />
*2012: Jenks Middle School<br />
<br />
==National Competition==<br />
<br />
In the national competition, Oklahoma is usually ranked in the middle, often scoring in the high 20s to high 30s. The best Oklahoma has ever done was in the second MathCounts year, with a student making first place individual and the team as 3rd.<br />
<br />
===AoPSers from Oklahoma who Made Nationals===<br />
<br />
Note: a strikethrough through the year represents that person made nationals because of countdown (i.e. ranked 5th or lower on written), and grayed out years means that person was ranked 4th written but lost countdown.<br />
<br />
*ILoveYouMC (2015, 2016)<br />
*guluguluga (2015)<br />
*NormanWho (2014, 2015)<br />
*saagar (<font color="gray">2014</font>, 2015)<br />
*clueless (<strike>2014</strike>)<br />
*hesa57 (<font color="gray">2013</font>, 2014)<br />
*yamiosum (<strike>2013</strike>, 2014)<br />
*Bosco7 (2012, 2013)<br />
*guilou25 (2012)<br />
*Zman104 (2012)<br />
*tchonka97 (2011, 2012)<br />
*garfielddisco123 (2011)<br />
*jonathanchou1711 (2010)<br />
<br />
==External Links==<br />
<br />
*[http://mathcountsok.com/ Oklahoma MathCounts Official Site]<br />
<br />
==See Also==<br />
<br />
*[http://artofproblemsolving.com/wiki/index.php/Oklahoma_mathematics_competitions Oklahoma Mathematics Competitions]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=Oklahoma_MathCounts&diff=77618Oklahoma MathCounts2016-03-17T00:43:30Z<p>Doitsudoitsu: stop stating trivial stuff goerge</p>
<hr />
<div>==Regional Competition==<br />
<br />
Oklahoma calls chapter competition as regionals. There are five distinct regions. Each region competes on a certain date.<br />
*Central: first weekend of February or last weekend of January<br />
*East central: one week after central<br />
*Eastern: two weeks after central<br />
*Northwestern: three weeks after central<br />
*Southwestern: four weeks after central<br />
<br />
Eastern region has been eliminated in 2015. It is uncertain about their existence in the future.<br />
<br />
The most competitive of these five regions are the ones with Oklahoma's two major metropolis: east central (Tulsa) and central (Oklahoma City/Norman).<br />
<br />
The selection process for advancing towards state competition is the same as all states. Countdown round is not used to determine state qualification.<br />
<br />
==State Competition==<br />
<br />
State competition is usually held on the first weekend of March. Approximately <math>80-88</math> students compete each year. Countdown round is official.<br />
<br />
===Past State Competition Winners===<br />
<br />
*2016: Vincent Li<br />
*2015: Vincent Li (Whittier Middle School)<br />
*2014: George Wang (Jenks Middle School)<br />
*2013: Amber Bick (Jenks Middle School)<br />
*2012: Thatcher Chonka (Metro Christian Academy)<br />
<br />
===Past State Competition Team Winners===<br />
<br />
*2016: Whittier Middle School<br />
*2015: Whittier Middle School<br />
*2014: Whittier Middle School<br />
*2013: Jenks Middle School<br />
*2012: Jenks Middle School<br />
<br />
==National Competition==<br />
<br />
In the national competition, Oklahoma is usually ranked in the middle, often scoring in the high 20s to high 30s. The best Oklahoma has ever done was in the second MathCounts year, with a student making first place individual and the team as 3rd.<br />
<br />
===AoPSers from Oklahoma who Made Nationals===<br />
<br />
Note: a strikethrough through the year represents that person made nationals because of countdown (i.e. ranked 5th or lower on written), and grayed out years means that person was ranked 4th written but lost countdown (hence, "got trolled on countdown").<br />
<br />
*ILoveYouMC (2015, 2016)<br />
*guluguluga (2015)<br />
*NormanWho (2014, 2015)<br />
*saagar (<font color="gray">2014</font>, 2015)<br />
*clueless (<strike>2014</strike>)<br />
*hesa57 (<font color="gray">2013</font>, 2014)<br />
*yamiosum (<strike>2013</strike>, 2014)<br />
*Bosco7 (2012, 2013)<br />
*guilou25 (2012)<br />
*Zman104 (2012)<br />
*tchonka97 (2011, 2012)<br />
*garfielddisco123 (2011)<br />
*jonathanchou1711 (2010)<br />
<br />
==External Links==<br />
<br />
*[http://mathcountsok.com/ Oklahoma MathCounts Official Site]<br />
<br />
==See Also==<br />
<br />
*[http://artofproblemsolving.com/wiki/index.php/Oklahoma_mathematics_competitions Oklahoma Mathematics Competitions]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=77617User:Phi ftw16182016-03-17T00:36:46Z<p>Doitsudoitsu: /* Vandalism Space */ rqqwq</p>
<hr />
<div>Apparently I get a user page! Fun!<br />
<br />
==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
<br />
The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
<br />
Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
<br />
The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
<br />
In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
<br />
===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
<br />
===Phi IRL===<br />
Phi is going to AwesomeMath 2016 at Puget Sound. He has made MATHCOUNTS State twice, but as for his competition results... haha, that's a nice joke. There aren't any notable ones.<br />
<br />
==AoPS Resource Usage==<br />
===FTW===<br />
Phi does play FTW occasionally, although when he does, it usually does not go well. His rating is around 1400, although that may change because after his MATHCOUNTS career, he will probably end up getting worse at speed mathematics. Compared to other AoPSers who are considered to be 'pro', phi_ftw1618 looks like a very bad FTW competitor.<br />
===Alcumus===<br />
phi_ftw1618 played a lot of Alcumus in preparation for his MATHCOUNTS and AMC 8 competitions. He eventually ended up mastering every topic, but does not use Alcumus very much right now except in last-minute preparation for some contests. He also does use Alcumus when he's bored at school, which happens surprisingly often.<br />
===MATHCOUNTS Trainer===<br />
phi_ftw1618 barely used MATHCOUNTS trainer except for getting school and chapter-level problems nailed because he prefers the Alcumus approach. He does have access to all 4 levels of problems, but still prefers Alcumus.<br />
===Reaper===<br />
phi_ftw1618 has tried numerous times to do well in Reaper, but has failed every time, with his best finish being a 9th place. He now thinks that Reaper is a waste of time unless the time between reaps is an hour or less, as otherwise, a reap becomes too valuable.<br />
===Greed Control===<br />
phi_ftw1618 is surprisingly bad at consistently inputting (relatively) small integers into a computer. Thus, he is quite bad at Greed Control as well. This is quite unfortunate, as it's easier on his sleep schedule to do well on Greed Control than Reaper.<br />
<br />
==Community==<br />
===Forums===<br />
phi_ftw1618 is on the forums a lot, possibly more than he should be. He usually uses the forums for both math and as a message board. Moreover, he also spends (probably too much) time with pandabear10 in various locations. He also plays on the Games forums, although currently makes it a rule of thumb to never post on either the Fun Factory or Frivolous Forum. He somehow has amassed 1183 posts despite not having more than 400 posts in any post-counting forum. <br />
===Blog===<br />
phi_ftw1618 runs a blog which is known mostly as [http://artofproblemsolving.com/community/c74051 the Phi Blog]. While it started as "a dumping ground for philosophy nonsense", it became a place for him to post anything and everything on a daily basis. It is now currently one of the few blogs on the blogroll that update daily (with three contributors for backup) and usually more often on days when he feels like it. The blog is used for everything that he needs, that is, he only owns the one blog, plus a forgotten one that is more public, but rarely used.<br />
<br />
The CSS for the blog was designed by NeoMathematicalKid, and is the result of phi_ftw1618 spending too much time looking at NMK's github for AoPS blogs.<br />
<br />
The blog was originally created 5/5/15, and currently has over 6000 views, 500+ comments, and 100+ shouts, which was the result of an unfortunate CSS accident that was later resolved, but still is quite buggy. He intends to repair this when he has time. However, he doesn't usually have time.<br />
<br />
==Trivia==<br />
<br />
*Phi also participates in Science Olympiad.<br />
*He has met pandabear10, Xinyan, and goseahawks in real life.<br />
*Phi sometimes refers to himself as phi IRL.<br />
*He also pronounces AoPS like "ay-ops" not "Ay-oh-pee-ess".<br />
*Phi speaks French.<br />
*Phi has run out of random facts to give you.<br />
<br />
==Crowdsourced Section==<br />
<br />
haha funny as if anyone will ever read this<br />
If you want to get a post into this section (short comment or so) post on my blog. I think I put something there (might be wrong).<br />
<br />
==Vandalism Space==<br />
ANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTiANTi</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=77602User:Phi ftw16182016-03-16T22:50:33Z<p>Doitsudoitsu: /* Vandalism Space */</p>
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<div>Apparently I get a user page! Fun!<br />
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==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
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The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
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Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
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The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
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In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
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===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
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==Vandalism Space==<br />
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Vandalism Space- this is designed to let edit vandals edit my page in a controlled environment. Comments made here will be deleted at phi_ftw1618's discretion.<br />
feel free to vandalize this as you wish.<br />
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joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681 joey8189681</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Phi_ftw1618&diff=77599User:Phi ftw16182016-03-16T22:45:21Z<p>Doitsudoitsu: qwrwerqwqcrqcqwre</p>
<hr />
<div>Apparently I get a user page! Fun!<br />
<br />
==About Phi==<br />
===Username Info===<br />
phi_ftw1618's username is unique in that he managed to insert an underscore into it, which makes typing his username (phi_ftw1618) a major pain to people who type less than 90 wpm (like most people). Thus, most of the time, people refer to him as phi, phi_ftw, or phiftw.<br />
<br />
The origin of the username comes from his first few times on FTW, which had been recommended to him as a resource by his MATHCOUNTS team. As it turned out, playing as a guest was hugely inconvenient without chat, and people kept quitting on him. Thus, he created an account with AoPS.<br />
<br />
Now, he wanted to choose a username that sounded like most. Thus, since he figured that there were a bunch of 'pi' usernames, he would create a phi username, representing the golden ratio, <math>\phi=\frac{1+\sqrt{5}}{2}</math>. Since the only reason that he originally had this account was FTW, he added the 'ftw' part, and for no apparent reason, put an underscore in between, not knowing how inconvenient it was to type an underscore. Then he appended the 1618, the first four digits of the aforementioned golden ratio.<br />
<br />
The username is officially pronounced "phi-eff-tee-double you-sixteen-eighteen", according to him. Others have pronounced it "phi-ftw-one-six-one-eight" and "phi".<br />
<br />
In fact, he is usually referenced as phi, and goes by such in most forums. Usage of his formal username is rare unless in a formal/official situation, which arises rarely.<br />
<br />
===Personal Info===<br />
phi_ftw1618 does not like stalkers.<br />
<br />
==Vandalism Space==<br />
<br />
Vandalism Space- this is designed to let edit vandals edit my page in a controlled environment. Comments made here will be deleted at phi_ftw1618's discretion.<br />
feel free to vandalize this as you wish.<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]<br />
[quote=zaiyo28]Hi, just letting you know as a friendly reminder not to revive topics that are over a year old without having a legitimate question<br />
Thanks.[/quote]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=Oklahoma_MathCounts&diff=77449Oklahoma MathCounts2016-03-07T02:34:46Z<p>Doitsudoitsu: george is very salty that he did not qual in 2013</p>
<hr />
<div>==Regional Competition==<br />
<br />
Oklahoma calls chapter competition as regionals. There are five distinct regions. Each region competes on a certain date.<br />
*Central: first weekend of February or last weekend of January<br />
*East central: one week after central<br />
*Eastern: two weeks after central<br />
*Northwestern: three weeks after central<br />
*Southwestern: four weeks after central<br />
<br />
Eastern region has been eliminated in 2015. It is uncertain about their existence in the future.<br />
<br />
The most competitive of these five regions are the ones with Oklahoma's two major metropolis: east central (Tulsa) and central (Oklahoma City/Norman).<br />
<br />
The selection process for advancing towards state competition is the same as all states. Countdown round is not used to determine state qualification.<br />
<br />
==State Competition==<br />
<br />
State competition is usually held on the first weekend of March. Approximately <math>80-88</math> students compete each year. Countdown round is official and has caused fourth place written to not make nationals.<br />
<br />
===Past State Competition Winners===<br />
<br />
*2015: Vincent Li (Whittier Middle School)<br />
*2014: George Wang (Jenks Middle School)<br />
*2013: Amber Bick (Jenks Middle School)<br />
*2012: Thatcher Chonka (Metro Christian Academy)<br />
<br />
===Past State Competition Team Winners===<br />
<br />
*2015: Whittier Middle School<br />
*2014: Whittier Middle School<br />
*2013: Jenks Middle School<br />
*2012: Jenks Middle School<br />
<br />
==National Competition==<br />
<br />
In the national competition, Oklahoma is usually ranked in the middle, often scoring in the high 20s to high 30s. The best Oklahoma has ever done was in the second MathCounts year, with a student making first place individual and the team as 3rd.<br />
<br />
===AoPSers from Oklahoma who Made Nationals===<br />
<br />
Note: a strikethrough through the year represents that person made nationals because of countdown (i.e. ranked 5th or lower on written), and grayed out years means that person was ranked 4th written but lost countdown.<br />
*ILoveYouMC (2015)<br />
*guluguluga (2015)<br />
*NormanWho (2014, 2015)<br />
*saagar (<font color="gray">2014</font>, 2015)<br />
*clueless (<strike>2014</strike>)<br />
*hesa57 (<font color="gray">2013</font>, 2014)<br />
*yamiosum (<strike>2013</strike>, 2014)<br />
*Bosco7 (2012, 2013)<br />
*guilou25 (2012)<br />
*Zman104 (2012)<br />
*tchonka97 (2011, 2012)<br />
*garfielddisco123 (2011)<br />
*jonathanchou1711 (2010)<br />
<br />
==External Links==<br />
<br />
*[http://mathcountsok.com/ Oklahoma MathCounts Official Site]<br />
<br />
==See Also==<br />
<br />
*[http://artofproblemsolving.com/wiki/index.php/Oklahoma_mathematics_competitions Oklahoma Mathematics Competitions]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2016_AIME_I_Problems&diff=773172016 AIME I Problems2016-03-04T22:32:25Z<p>Doitsudoitsu: whats with the latex</p>
<hr />
<div>{{AIME Problems|year=2016|n=I}}<br />
<br />
==Problem 1==<br />
For <math>-1<r<1</math>, let <math>S(r)</math> denote the sum of the geometric series <cmath>12+12r+12r^2+12r^3+\cdots .</cmath> Let <math>a</math> between <math>-1</math> and <math>1</math> satisfy <math>S(a)S(-a)=2016</math>. Find <math>S(a)+S(-a)</math>. <br />
<br />
[[2016 AIME I Problems/Problem 1 | Solution]]<br />
<br />
==Problem 2==<br />
Two dice appear to be normal dice with their faces numbered from <math>1</math> to <math>6</math>, but each die is weighted so that the probability of rolling the number <math>k</math> is directly proportional to <math>k</math>. The probability of rolling a <math>7</math> with this pair of dice is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
[[2016 AIME I Problems/Problem 2 | Solution]]<br />
<br />
==Problem 3==<br />
A regular icosahedron is a <math>20</math>-faced solid where each face is an equilateral triangle and five triangles meet at every vertex. The regular icosahedron shown below has one vertex at the top, one vertex at the bottom, an upper pentagon of five vertices all adjacent to the top vertex and all in the same horizontal plane, and a lower pentagon of five vertices all adjacent to the bottom vertex and all in another horizontal plane. Find the number of paths from the top vertex to the bottom vertex such that each part of a path goes downward or horizontally along an edge of the icosahedron, and no vertex is repeated. <br />
<br />
[[2016 AIME I Problems/Problem 3 | Solution]]<br />
<br />
==Problem 4==<br />
A right prism with height <math>h</math> has bases that are regular hexagons with sides of length <math>12</math>. A vertex <math>A</math> of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain <math>A</math> measures <math>60^{\circ}</math>. Find <math>h^2</math>.<br />
<br />
[[2016 AIME I Problems/Problem 4 | Solution]]<br />
<br />
==Problem 5==<br />
Anh read a book. On the first day she read <math>n</math> pages in <math>t</math> minutes, where <math>n</math> and <math>t</math> are positive integers. On the second day Anh read <math>n + 1</math> pages in <math>t + 1</math> minutes. Each day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely read the <math>374</math> page book. It took her a total of <math>319</math> minutes to read the book. Find <math>n + t</math>.<br />
<br />
[[2016 AIME I Problems/Problem 5 | Solution]]<br />
<br />
==Problem 6==<br />
<br />
In <math>\triangle ABC</math> let <math>I</math> be the center of the inscribed circle, and let the bisector of <math>\angle ACB</math> intersect <math>\overline{AB}</math> at <math>L</math>. The line through <math>C</math> and <math>L</math> intersects the circumscribed circle of <math>\triangle ABC</math> at the two points <math>C</math> and <math>D</math>. If <math>LI=2</math> and <math>LD=3</math>, then <math>IC= \frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>.<br />
<br />
[[2016 AIME I Problems/Problem 6 | Solution]]<br />
<br />
==Problem 7==<br />
For integers <math>a</math> and <math>b</math> consider the complex number <cmath>\frac{\sqrt{ab+2016}}{ab+100}-\left(\frac{\sqrt{|a+b|}}{ab+100}\right)i.</cmath> Find the number of ordered pairs of integers <math>(a,b)</math> such that this complex number is a real number.<br />
<br />
[[2016 AIME I Problems/Problem 7 | Solution]]<br />
<br />
==Problem 8==<br />
For a permutation <math>p = (a_1,a_2,\ldots,a_9)</math> of the digits <math>1,2,\ldots,9</math>, let <math>s(p)</math> denote the sum of the three <math>3</math>-digit numbers <math>a_1a_2a_3</math>, <math>a_4a_5a_6</math>, and <math>a_7a_8a_9</math>. Let <math>m</math> be the minimum value of <math>s(p)</math> subject to the condition that the units digit of <math>s(p)</math> is <math>0</math>. Let <math>n</math> denote the number of permutations <math>p</math> with <math>s(p) = m</math>. Find <math>|m - n|</math>.<br />
<br />
[[2016 AIME I Problems/Problem 8 | Solution]]<br />
<br />
==Problem 9==<br />
Triangle <math>ABC</math> has <math>AB=40,AC=31,</math> and <math>\sin{A}=\frac{1}{5}</math>. This triangle is inscribed in rectangle <math>AQRS</math> with <math>B</math> on <math>\overline{QR}</math> and <math>C</math> on <math>\overline{RS}</math>. Find the maximum possible area of <math>AQRS</math>.<br />
<br />
[[2016 AIME I Problems/Problem 9 | Solution]]<br />
<br />
==Problem 10==<br />
<br />
A strictly increasing sequence of positive integers <math>a_1</math>, <math>a_2</math>, <math>a_3</math>, <math>\cdots</math> has the property that for every positive integer <math>k</math>, the subsequence <math>a_{2k-1}</math>, <math>a_{2k}</math>, <math>a_{2k+1}</math> is geometric and the subsequence <math>a_{2k}</math>, <math>a_{2k+1}</math>, <math>a_{2k+2}</math> is arithmetic. Suppose that <math>a_{13} = 2016</math>. Find <math>a_1</math>.<br />
<br />
[[2016 AIME I Problems/Problem 10 | Solution]]<br />
<br />
==Problem 11==<br />
<br />
Let <math>P(x)</math> be a nonzero polynomial such that <math>(x-1)P(x+1)=(x+2)P(x)</math> for every real <math>x</math>, and <math>\left(P(2)\right)^2 = P(3)</math>. Then <math>P(\tfrac72)=\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>.<br />
<br />
[[2016 AIME I Problems/Problem 11 | Solution]]<br />
<br />
==Problem 12==<br />
Find the least positive integer <math>m</math> such that <math>m^2 - m + 11</math> is a product of at least four not necessarily distinct primes. <br />
<br />
[[2016 AIME I Problems/Problem 12 | Solution]]<br />
<br />
==Problem 13==<br />
Freddy the frog is jumping around the coordinate plane searching for a river, which lies on the horizontal line <math>y = 24</math>. A fence is located at the horizontal line <math>y = 0</math>. On each jump Freddy randomly chooses a direction parallel to one of the coordinate axes and moves one unit in that direction. When he is at a point where <math>y=0</math>, with equal likelihoods he chooses one of three directions where he either jumps parallel to the fence or jumps away from the fence, but he never chooses the direction that would have him cross over the fence to where <math>y < 0</math>. Freddy starts his search at the point <math>(0, 21)</math> and will stop once he reaches a point on the river. Find the expected number of jumps it will take Freddy to reach the river.<br />
<br />
[[2016 AIME I Problems/Problem 13 | Solution]]<br />
<br />
==Problem 14==<br />
<br />
Centered at each lattice point in the coordinate plane are a circle radius <math>\frac{1}{10}</math> and a square with sides of length <math>\frac{1}{5}</math> whose sides are parallel to the coordinate axes. The line segment from <math>(0,0)</math> to <math>(1001, 429)</math> intersects <math>m</math> of the squares and <math>n</math> of the circles. Find <math>m + n</math>.<br />
<br />
[[2016 AIME I Problems/Problem 14 | Solution]]<br />
<br />
==Problem 15==<br />
<br />
Circles <math>\omega_1</math> and <math>\omega_2</math> intersect at points <math>X</math> and <math>Y</math>. Line <math>\ell</math> is tangent to <math>\omega_1</math> and <math>\omega_2</math> at <math>A</math> and <math>B</math>, respectively, with line <math>AB</math> closer to point <math>X</math> than to <math>Y</math>. Circle <math>\omega</math> passes through <math>A</math> and <math>B</math> intersecting <math>\omega_1</math> again at <math>D \neq A</math> and intersecting <math>\omega_2</math> again at <math>C \neq B</math>. The three points <math>C</math>, <math>Y</math>, <math>D</math> are collinear, <math>XC = 67</math>, <math>XY = 47</math>, and <math>XD = 37</math>. Find <math>AB^2</math>.<br />
<br />
[[2016 AIME I Problems/Problem 15 | Solution]]<br />
<br />
{{AIME box|year=2016|n=I|before=[[2015 AIME II]]|after=[[2016 AIME II]]}}<br />
{{MAA Notice}}</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2016_AMC_10B_Problems/Problem_23&diff=766142016 AMC 10B Problems/Problem 232016-02-21T16:03:45Z<p>Doitsudoitsu: an answer is not a solution; the user does not deserve credit for this.</p>
<hr />
<div>==Problem==<br />
<br />
In regular hexagon <math>ABCDEF</math>, points <math>W</math>, <math>X</math>, <math>Y</math>, and <math>Z</math> are chosen on sides <math>\overline{BC}</math>, <math>\overline{CD}</math>, <math>\overline{EF}</math>, and <math>\overline{FA}</math> respectively, so lines <math>AB</math>, <math>ZW</math>, <math>YX</math>, and <math>ED</math> are parallel and equally spaced. What is the ratio of the area of hexagon <math>WCXYFZ</math> to the area of hexagon <math>ABCDEF</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{10}{27}\qquad\textbf{(C)}\ \frac{11}{27}\qquad\textbf{(D)}\ \frac{4}{9}\qquad\textbf{(E)}\ \frac{13}{27}</math><br />
<br />
<br />
==Solution==<br />
<math>\textbf{(C)}\ \frac{11}{27}</math></div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2016_AMC_10B_Problems/Problem_3&diff=766022016 AMC 10B Problems/Problem 32016-02-21T15:56:53Z<p>Doitsudoitsu: basic solution; someone should add detailed edits in; this was rushed.</p>
<hr />
<div>==Problem==<br />
<br />
Let <math>x=-2016</math>. What is the value of <math>\bigg|</math> <math>|x|-x|-|x|</math> <math>\bigg|</math> <math>-x</math>?<br />
<br />
<math>\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048</math><br />
<br />
==Solution==<br />
<math>|-2016|-(-2016) \implies 2016+2016 \implies 4032</math>.<br />
<math>4032-|-2016| \implies 4032-2016 \implies 2016</math>.<br />
<math>|2016|=2016</math>.<br />
<math>2016-(-2016) \implies 2016+2016=\boxed{4032}</math>.</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=AMC_10_Problems_and_Solutions&diff=75042AMC 10 Problems and Solutions2016-02-03T16:39:06Z<p>Doitsudoitsu: adding in 2016</p>
<hr />
<div>[[AMC 10]] problems and solutions.<br />
<br />
{| class="wikitable"<br />
|-<br />
! Year || Test A || Test B<br />
|-<br />
| 2016 || [[2016 AMC 10A | AMC 10A]] ||<br />
|-<br />
| 2015 || [[2015 AMC 10A | AMC 10A]] || [[2015 AMC 10B | AMC 10B]]<br />
|-<br />
| 2014 || [[2014 AMC 10A | AMC 10A]] || [[2014 AMC 10B | AMC 10B]]<br />
|-<br />
| 2013 || [[2013 AMC 10A | AMC 10A]] || [[2013 AMC 10B | AMC 10B]]<br />
|-<br />
| 2012 || [[2012 AMC 10A | AMC 10A]] || [[2012 AMC 10B | AMC 10B]]<br />
|-<br />
| 2011 || [[2011 AMC 10A | AMC 10A]] || [[2011 AMC 10B | AMC 10B]]<br />
|-<br />
| 2010 || [[2010 AMC 10A | AMC 10A]] || [[2010 AMC 10B | AMC 10B]]<br />
|-<br />
| 2009 || [[2009 AMC 10A | AMC 10A]] || [[2009 AMC 10B | AMC 10B]]<br />
|-<br />
| 2008 || [[2008 AMC 10A | AMC 10A]] || [[2008 AMC 10B | AMC 10B]]<br />
|-<br />
| 2007 || [[2007 AMC 10A | AMC 10A]] || [[2007 AMC 10B | AMC 10B]]<br />
|-<br />
| 2006 || [[2006 AMC 10A | AMC 10A]] || [[2006 AMC 10B | AMC 10B]]<br />
|-<br />
| 2005 || [[2005 AMC 10A | AMC 10A]] || [[2005 AMC 10B | AMC 10B]]<br />
|-<br />
| 2004 || [[2004 AMC 10A | AMC 10A]] || [[2004 AMC 10B | AMC 10B]]<br />
|-<br />
| 2003 || [[2003 AMC 10A | AMC 10A]] || [[2003 AMC 10B | AMC 10B]]<br />
|-<br />
| 2002 || [[2002 AMC 10A | AMC 10A]] || [[2002 AMC 10B | AMC 10B]]<br />
|-<br />
| 2001 || [[2001 AMC 10 | AMC 10]] ||<br />
|-<br />
| 2000 || [[2000 AMC 10 | AMC 10]] ||<br />
|}<br />
<br />
== Resources ==<br />
* [[American Mathematics Competitions]]<br />
* [[AMC Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
[[Category:Math Contest Problems]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Hesa57&diff=73400User:Hesa572015-12-01T14:18:39Z<p>Doitsudoitsu: yay</p>
<hr />
<div>Hi<br />
<br />
I am in 10th grade, and I live in Oklahoma.<br />
<br />
Below is some info about me.<br />
<br />
==9th Grade==<br />
<br />
===Accomplishments===<br />
<br />
*1st state MathLeague (mathleague.com; score 34/36)<br />
*1st state AMC 10 (120)<br />
*1st state AIME (8)<br />
*State winner (index 200) + USAJMO qualifier<br />
<br />
===Goals===<br />
<br />
Key: Goal, actual<br />
<br />
*MathLeague: 32/36 and 2nd state, 34/36 and 1st in state<br />
*AMC 10 A: 120 and 2nd state, 120 and 1st state (freebie)<br />
*AIME: 5, 8<br />
*USAJMO: 1/42, 5/42<br />
*Math Kangaroo: state winner (because I'm the only 9th grader in the state that took it), 113<br />
<br />
==8th Grade==<br />
<br />
===Accomplishments===<br />
<br />
MathCounts:<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Written Score'''<br />
! scope="col" | '''Written Ranking'''<br />
! scope="col" | '''Ranking After Countdown'''<br />
! scope="col" | '''Team Score'''<br />
! scope="col" | '''Team Rank'''<br />
|-<br />
! scope="row" | '''Jenks Mock'''<br />
| <math>27+14=41</math><br />
| <math>1</math><br />
| <math>2</math><br />
| <math>10</math><br />
| <math>1</math><br />
|-<br />
! scope="row" | '''School'''<br />
| <math>27(?)+16=43</math><br />
| <math>2</math><br />
| <math>3</math><br />
| <math>10</math> (?)<br />
| <math>2</math><br />
|-<br />
! scope="row" | '''Chapter'''<br />
| Some fail score<br />
| <math>4</math><br />
| <math>4</math> (won, then lost to younger brother)<br />
| <math>10</math> (guess on #10)<br />
| <math>1</math><br />
|-<br />
! scope="row" | '''State'''<br />
| <math>20+10=30</math><br />
| <math>1</math><br />
| <math>1</math><br />
| <math>4</math><br />
| <math>2</math><br />
|-<br />
! scope="row" | '''Nationals'''<br />
| <math>15+10=25</math><br />
| <math>110</math><br />
|<br />
| Forgot<br />
| Fail<br />
|}<br />
<br />
*AMC 8: 25<br />
*Math Kangaroo: 115, 4th nationally<br />
*OSSM: 1st in division 4<br />
<br />
===Goals===<br />
<br />
MathCounts:<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Written Score'''<br />
! scope="col" | '''Written Ranking'''<br />
! scope="col" | '''Ranking After Countdown'''<br />
! scope="col" | '''Team Score'''<br />
! scope="col" | '''Team Rank'''<br />
|-<br />
! scope="row" | '''Jenks Mock'''<br />
| <math>25+16=41</math><br />
| <math>1</math><br />
| <math>2</math><br />
| <math>10</math><br />
| <math>1</math><br />
|-<br />
! scope="row" | '''School'''<br />
| <math>25+16=41</math><br />
| <math>1</math><br />
| <math>2</math><br />
| <math>10</math><br />
| <math>1</math><br />
|-<br />
! scope="row" | '''Chapter'''<br />
| None<br />
| <math>3</math><br />
| <math>4</math><br />
| <math>9</math><br />
| <math>1</math><br />
|-<br />
! scope="row" | '''State'''<br />
| None<br />
| <math>3</math><br />
| <math>4</math><br />
| <math>7</math><br />
| <math>1</math><br />
|-<br />
! scope="row" | '''Nationals'''<br />
| None<br />
| Top 56<br />
|<br />
| None<br />
| Top 30<br />
|}<br />
<br />
*AMC 8: 25<br />
*MathKangaroo: top 10 nationally<br />
*OSSM: 1st in division 4<br />
<br />
==Future Goals==<br />
<br />
===10th Grade===<br />
<br />
Since I met/exceeded every single goal this year, I decided to make impossible goals next year.<br />
<br />
*141 AMC 10<br />
*111 AMC 12<br />
*12 AIME<br />
*USAJMO 21+<br />
*120 MathKangaroo<br />
*MathLeague 36/36<br />
<br />
===11th Grade===<br />
<br />
*141 AMC 12<br />
*12 AIME<br />
*USAMO 20+<br />
*120 MathKangaroo<br />
*MathLeague 36<br />
<br />
More impossible goals<br />
<br />
===12th Grade===<br />
<br />
*144 AMC 12<br />
*13+ AIME<br />
*USAMO 25+<br />
*120 MathKangaroo<br />
*MathLeague: don't do it; too trivial</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Doitsudoitsu&diff=73399User:Doitsudoitsu2015-12-01T14:15:51Z<p>Doitsudoitsu: who the heck edited this</p>
<hr />
<div>doitsu is coming for yoo</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2014_AIME_I_Problems&diff=729452014 AIME I Problems2015-11-22T17:19:08Z<p>Doitsudoitsu: grammar</p>
<hr />
<div>{{AIME Problems|year=2014|n=I}}<br />
<br />
==Problem 1==<br />
The 8 eyelets for the lace of a sneaker all lie on a rectangle, four equally spaced on each of the longer sides. The rectangle has a width of 50 mm and a length of 80 mm. There is one eyelet at each vertex of the rectangle. The lace itself must pass between the vertex eyelets along a width side of the rectangle and then crisscross between successive eyelets until it reaches the two eyelets at the other width side of the rectangle as shown. After passing through these final eyelets, each of the ends of the lace must extend at least 200 mm farther to allow a knot to be tied. Find the minimum length of the lace in millimeters. <br />
<br />
<asy><br />
size(200);<br />
defaultpen(linewidth(0.7));<br />
path laceL=(-20,-30)..tension 0.75 ..(-90,-135)..(-102,-147)..(-152,-150)..tension 2 ..(-155,-140)..(-135,-40)..(-50,-4)..tension 0.8 ..origin;<br />
path laceR=reflect((75,0),(75,-240))*laceL;<br />
draw(origin--(0,-240)--(150,-240)--(150,0)--cycle,gray);<br />
for(int i=0;i<=3;i=i+1)<br />
{<br />
path circ1=circle((0,-80*i),5),circ2=circle((150,-80*i),5);<br />
unfill(circ1); draw(circ1);<br />
unfill(circ2); draw(circ2);<br />
}<br />
draw(laceL--(150,-80)--(0,-160)--(150,-240)--(0,-240)--(150,-160)--(0,-80)--(150,0)^^laceR,linewidth(1));</asy><br />
[[2014 AIME I Problems/Problem 1|Solution]]<br />
<br />
==Problem 2== <br />
<br />
An urn contains <math>4</math> green balls and <math>6</math> blue balls. A second urn contains <math>16</math> green balls and <math>N</math> blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is <math>0.58</math>. Find <math>N</math>.<br />
<br />
[[2014 AIME I Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
Find the number of rational numbers <math>r</math>, <math>0<r<1,</math> such that when <math>r</math> is written as a fraction in lowest terms, the numerator and the denominator have a sum of <math>1000</math>.<br />
<br />
[[2014 AIME I Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
Jon and Steve ride their bicycles along a path that parallels two side-by-side train tracks running the east/west direction. Jon rides east at <math>20</math> miles per hour, and Steve rides west at <math>20</math> miles per hour. Two trains of equal length, traveling in opposite directions at constant but different speeds each pass the two riders. Each train takes exactly <math>1</math> minute to go past Jon. The westbound train takes <math>10</math> times as long as the eastbound train to go past Steve. The length of each train is <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
[[2014 AIME I Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Let the set <math>S = \{P_1, P_2, \dots, P_{12}\}</math> consist of the twelve vertices of a regular <math>12</math>-gon. A subset <math>Q</math> of <math>S</math> is called communal if there is a circle such that all points of <math>Q</math> are inside the circle, and all points of <math>S</math> not in <math>Q</math> are outside of the circle. How many communal subsets are there? (Note that the empty set is a communal subset.)<br />
<br />
[[2014 AIME I Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
The graphs <math>y = 3(x-h)^2 + j</math> and <math>y = 2(x-h)^2 + k</math> have y-intercepts of <math>2013</math> and <math>2014</math>, respectively, and each graph has two positive integer x-intercepts. Find <math>h</math>.<br />
<br />
[[2014 AIME I Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
Let <math>w</math> and <math>z</math> be complex numbers such that <math>|w| = 1</math> and <math>|z| = 10</math>. Let <math>\theta = \arg \left(\tfrac{w-z}{z}\right) </math>. The maximum possible value of <math>\tan^2 \theta</math> can be written as <math>\tfrac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. (Note that <math>\arg(w)</math>, for w <math>\neq 0</math>, denotes the measure of the angle that the ray from <math>0</math> to <math>w</math> makes with the positive real axis in the complex plane.<br />
<br />
[[2014 AIME I Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
The positive integers <math>N</math> and <math>N^2</math> both end in the same sequence of four digits <math>abcd</math> when written in base 10, where digit <math>a</math> is not zero. Find the three-digit number <math>abc</math>.<br />
<br />
[[2014 AIME I Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
Let <math>x_1< x_2 < x_3</math> be the three real roots of the equation <math>\sqrt{2014} x^3 - 4029x^2 + 2 = 0</math>. Find <math>x_2(x_1+x_3)</math>.<br />
<br />
[[2014 AIME I Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
A disk with radius <math>1</math> is externally tangent to a disk with radius <math>5</math>. Let <math>A</math> be the point where the disks are tangent, <math>C</math> be the center of the smaller disk, and <math>E</math> be the center of the larger disk. While the larger disk remains fixed, the smaller disk is allowed to roll along the outside of the larger disk until the smaller disk has turned through an angle of <math>360^\circ</math>. That is, if the center of the smaller disk has moved to the point <math>D</math>, and the point on the smaller disk that began at <math>A</math> has now moved to point <math>B</math>, then <math>\overline{AC}</math> is parallel to <math>\overline{BD}</math>. Then <math>\sin^2(\angle BEA)=\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
[[2014 AIME I Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
A token starts at the point <math>(0,0)</math> of an <math>xy</math>-coordinate grid and then makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of <math>|y|=|x|</math> is <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
[[2014 AIME I Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Let <math>A=\{1,2,3,4\}</math>, and <math>f</math> and <math>g</math> be randomly chosen (not necessarily distinct) functions from <math>A</math> to <math>A</math>. The probability that the range of <math>f</math> and the range of <math>g</math> are disjoint is <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m</math>.<br />
<br />
[[2014 AIME I Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
On square <math>ABCD</math>, points <math>E,F,G</math>, and <math>H</math> lie on sides <math>\overline{AB},\overline{BC},\overline{CD},</math> and <math>\overline{DA},</math> respectively, so that <math>\overline{EG} \perp \overline{FH}</math> and <math>EG=FH = 34</math>. Segments <math>\overline{EG}</math> and <math>\overline{FH}</math> intersect at a point <math>P</math>, and the areas of the quadrilaterals <math>AEPH, BFPE, CGPF,</math> and <math>DHPG</math> are in the ratio <math>269:275:405:411.</math> Find the area of square <math>ABCD</math>.<br />
<br />
<asy><br />
pair A = (0,sqrt(850));<br />
pair B = (0,0);<br />
pair C = (sqrt(850),0);<br />
pair D = (sqrt(850),sqrt(850));<br />
draw(A--B--C--D--cycle);<br />
dotfactor = 3;<br />
dot("$A$",A,dir(135));<br />
dot("$B$",B,dir(215));<br />
dot("$C$",C,dir(305));<br />
dot("$D$",D,dir(45));<br />
pair H = ((2sqrt(850)-sqrt(306))/6,sqrt(850));<br />
pair F = ((2sqrt(850)+sqrt(306)+7)/6,0);<br />
dot("$H$",H,dir(90));<br />
dot("$F$",F,dir(270));<br />
draw(H--F);<br />
pair E = (0,(sqrt(850)-6)/2);<br />
pair G = (sqrt(850),(sqrt(850)+sqrt(100))/2);<br />
dot("$E$",E,dir(180));<br />
dot("$G$",G,dir(0));<br />
draw(E--G);<br />
pair P = extension(H,F,E,G);<br />
dot("$P$",P,dir(60));<br />
label("$w$", intersectionpoint( A--P, E--H ));<br />
label("$x$", intersectionpoint( B--P, E--F ));<br />
label("$y$", intersectionpoint( C--P, G--F ));<br />
label("$z$", intersectionpoint( D--P, G--H ));</asy><br />
<br />
[[2014 AIME I Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
Let <math>m</math> be the largest real solution to the equation<br />
<br />
<cmath> \dfrac{3}{x-3} + \dfrac{5}{x-5} + \dfrac{17}{x-17} + \dfrac{19}{x-19} = x^2 - 11x - 4</cmath><br />
<br />
There are positive integers <math>a, b,</math> and <math>c</math> such that <math>m = a + \sqrt{b + \sqrt{c}}</math>. Find <math>a+b+c</math>.<br />
<br />
[[2014 AIME I Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
In <math>\triangle ABC, AB = 3, BC = 4,</math> and <math>CA = 5</math>. Circle <math>\omega</math> intersects <math>\overline{AB}</math> at <math>E</math> and <math>B, \overline{BC}</math> at <math>B</math> and <math>D,</math> and <math>\overline{AC}</math> at <math>F</math> and <math>G</math>. Given that <math>EF=DF</math> and <math>\frac{DG}{EG} = \frac{3}{4},</math> length <math>DE=\frac{a\sqrt{b}}{c},</math> where <math>a</math> and <math>c</math> are relatively prime positive integers, and <math>b</math> is a positive integer not divisible by the square of any prime. Find <math>a+b+c</math>.<br />
<br />
[[2014 AIME I Problems/Problem 15|Solution]]<br />
<br />
{{MAA Notice}}</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Doitsudoitsu&diff=72682User:Doitsudoitsu2015-11-01T14:45:45Z<p>Doitsudoitsu: </p>
<hr />
<div>doit su is coming for yoo</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=User:Doitsudoitsu&diff=72071User:Doitsudoitsu2015-09-16T02:42:24Z<p>Doitsudoitsu: testing if this is legal</p>
<hr />
<div>georgie porgie<br />
<br />
is editing my own page like this legal</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=Mock_AMC&diff=71492Mock AMC2015-08-09T02:58:35Z<p>Doitsudoitsu: added september one</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past AMC/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are less.<br />
<br />
== Past Mock AMCs ==<br />
Listed below are the Mock AMCs which have been hosted over AoPS in the past. All of these links are to message board threads.<br />
<br />
Note that the "level" column represents the original intended difficulty. In other words, if a person makes a mock AMC 12, the level would be "12", even if the problems themselves are much easier.<br />
<br />
=== 2003 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Level'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 12<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|}<br />
<br />
----<br />
<br />
=== 2004===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Level'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 12<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 12<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| beta<br />
| 12<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| JGeneson<br />
| 12<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| joml88<br />
| 12<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Silverfalcon<br />
| 11<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 8<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2005 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| joml88<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| Lucky707<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| white_horse_king88<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| Silverfalcon<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| amirhtlusa<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| amirhtlusa<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2006 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| chess64<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| mustafa<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| Anirudh<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| calc rulz<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| rnwang2<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2007 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| mysmartmouth<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| paladin8<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
<br />
|}<br />
<br />
----<br />
<br />
=== 2008 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC'''<br />
| Silverfalcon<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2009 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| gfour84<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2010 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|}<br />
<br />
-----<br />
<br />
=== 2011 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2012 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|}<br />
<br />
----<br />
<br />
=== 2013 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 6'''<br />
| rafa2be<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=566529&hilit=rafa2be%27s+mock+amc Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3331909#p3331909 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3343627#p3343627 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3343627#p3343627 Results/Discussion]<br />
|}<br />
<br />
----<br />
<br />
=== 2014 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 4'''<br />
| rafa2be<br />
| [http://www.artofproblemsolving.com/community/c5h566529p3410210 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3444509#p3444509 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3456490#p3456490 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3457387#p3457387 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| AlcumusGuy<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|}<br />
<br />
=== 2015 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10'''<br />
| droid347<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
|<br />
|-<br />
! scope = "row" |'"(Almost) September Mock AMC 10<br />
| checkmatetang<br />
| [http://www.artofproblemsolving.com/community/u240581h1126446p5208894 Initial Discussion]<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2015_AMC_10A_Problems&diff=714432015 AMC 10A Problems2015-08-03T19:33:12Z<p>Doitsudoitsu: </p>
<hr />
<div>==Problem 1==<br />
<br />
What is the value of <math>(2^0-1+5^2-0)^{-1}\times5?</math><br />
<br />
<math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{5}{24}\qquad\textbf{(E)}\ 25</math><br />
<br />
[[2015 AMC 10A Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
<br />
A box contains a collection of triangular and square tiles. There are <math>25</math> tiles in the box, containing <math>84</math> edges total. How many square tiles are there in the box?<br />
<br />
<math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11</math><br />
<br />
[[2015 AMC 10A Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?<br />
<br />
<math>\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24</math><br />
<br />
[[2015 AMC 10A Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
<br />
Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?<br />
<br />
<math> \textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Mr. Patrick teaches math to <math> 15 </math> students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was <math> 80 </math>. After he graded Payton's test, the test average became <math> 81 </math>. What was Payton's score on the test?<br />
<br />
<math> \textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}\ 94\qquad\textbf{(E)}\ 95 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
<br />
The sum of two positive numbers is <math> 5 </math> times their difference. What is the ratio of the larger number to the smaller number?<br />
<br />
<math> \textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}\ 2 \qquad\textbf{(E)}\ \frac{5}{2} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
<br />
How many terms are there in the arithmetic sequence <math>13</math>, <math>16</math>, <math>19</math>, . . ., <math>70</math>, <math>73</math>?<br />
<br />
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 21\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 60\qquad\textbf{(E)}\ 61 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be <math>2</math> : <math>1</math>?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 8 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
Two right circular cylinders have the same volume. The radius of the second cylinder is <math>10\%</math> more than the radius of the first. What is the relationship between the heights of the two cylinders?<br />
<br />
<math>\textbf{(A)}\ \text{The second height is } 10\% \text{ less than the first.} \\ \textbf{(B)}\ \text{The first height is } 10\% \text{ more than the second.}\\ \textbf{(C)}\ \text{The second height is } 21\% \text{ less than the first.} \\ \textbf{(D)}\ \text{The first height is } 21\% \text{ more than the second.}\\ \textbf{(E)}\ \text{The second height is } 80\% \text{ of the first.}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
<br />
How many rearrangements of <math>abcd</math> are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either <math>ab</math> or <math>ba</math>.<br />
<br />
<math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4</math><br />
<br />
[[2015 AMC 10A Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
<br />
The ratio of the length to the width of a rectangle is <math>4</math> : <math>3</math>. If the rectangle has diagonal of length <math>d</math>, then the area may be expressed as <math>kd^2</math> for some constant <math>k</math>. What is <math>k</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{2}{7}\qquad\textbf{(B)}\ \frac{3}{7}\qquad\textbf{(C)}\ \frac{12}{25}\qquad\textbf{(D)}\ \frac{16}{25}\qquad\textbf{(E)}\ \frac{3}{4}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Points <math>(\sqrt{\pi}, a)</math> and <math>(\sqrt{\pi}, b)</math> are distinct points on the graph of <math>y^2+x^4=2x^2y+1</math>. What is <math>|a-b|</math>?<br />
<br />
<math> \textbf{(A) }1\qquad\textbf{(B) }\dfrac{\pi}{2}\qquad\textbf{(C) }2\qquad\textbf{(D) }\sqrt{1+\pi}\qquad\textbf{(E) }1+\sqrt{\pi} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?<br />
<br />
<math> \textbf{(A) }3\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
<br />
The diagram below shows the circular face of a clock with radius <math>20</math> cm and a circular disk with radius <math>10</math> cm externally tangent to the clock face at <math>12</math> o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?<br />
<br />
<asy><br />
size(170);<br />
defaultpen(linewidth(0.9)+fontsize(13pt));<br />
draw(unitcircle^^circle((0,1.5),0.5));<br />
path arrow = origin--(-0.13,-0.35)--(-0.06,-0.35)--(-0.06,-0.7)--(0.06,-0.7)--(0.06,-0.35)--(0.13,-0.35)--cycle;<br />
for(int i=1;i<=12;i=i+1)<br />
{<br />
draw(0.9*dir(90-30*i)--dir(90-30*i));<br />
label("$"+(string) i+"$",0.78*dir(90-30*i));<br />
}<br />
dot(origin);<br />
draw(shift((0,1.87))*arrow);<br />
draw(arc(origin,1.5,68,30),EndArrow(size=12));<br />
</asy><br />
<br />
<math> \textbf{(A) }\mathrm{2 o'clock} \qquad\textbf{(B) }\mathrm{3 o'clock} \qquad\textbf{(C) }\mathrm{4 o'clock} \qquad\textbf{(D) }\mathrm{6 o'clock} \qquad\textbf{(E) }\mathrm{8 o'clock} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
Consider the set of all fractions <math>\tfrac{x}{y},</math> where <math>x</math> and <math>y</math> are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by <math>1</math>, the value of the fraction is increased by <math>10\%</math>?<br />
<br />
<math> \textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
If <math>y+4 = (x-2)^2, x+4 = (y-2)^2</math>, and <math>x \neq y</math>, what is the value of <math>x^2+y^2</math>?<br />
<br />
<math> \textbf{(A) }10\qquad\textbf{(B) }15\qquad\textbf{(C) }20\qquad\textbf{(D) }25\qquad\textbf{(E) }\text{30} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
A line that passes through the origin intersects both the line <math>x=1</math> and the line <math>y=1+\frac{\sqrt{3}}{3}x</math>. The three lines create an equilateral triangle. What is the perimeter of the triangle?<br />
<br />
<math> \textbf{(A) }2\sqrt{6}\qquad\textbf{(B) }2+2\sqrt{3}\qquad\textbf{(C) }6\qquad\textbf{(D) }3+2\sqrt{3}\qquad\textbf{(E) }6+\frac{\sqrt{3}}{3} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
Hexadecimal (base-16) numbers are written using numeric digits <math>0</math> through <math>9</math> as well as the letters <math>A</math> through <math>F</math> to represent <math>10</math> through <math>15</math>. Among the first <math>1000</math> positive integers, there are <math>n</math> whose hexadecimal representation contains only numeric digits. What is the sum of the digits of <math>n</math>?<br />
<br />
<math> \textbf{(A) }17\qquad\textbf{(B) }18\qquad\textbf{(C) }19\qquad\textbf{(D) }20\qquad\textbf{(E) }21 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
The isosceles right triangle <math>ABC</math> has right angle at <math>C</math> and area <math>12.5</math>. The rays trisecting <math>\angle ACB</math> intersect <math>AB</math> at <math>D</math> and <math>E</math>. What is the area of <math>\bigtriangleup CDE</math>?<br />
<br />
<math> \textbf{(A) }\dfrac{5\sqrt{2}}{3}\qquad\textbf{(B) }\dfrac{50\sqrt{3}-75}{4}\qquad\textbf{(C) }\dfrac{15\sqrt{3}}{8}\qquad\textbf{(D) }\dfrac{50-25\sqrt{3}}{2}\qquad\textbf{(E) }\dfrac{25}{6} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
<br />
A rectangle with positive integer side lengths in <math>\text{cm}</math> has area <math>A</math> <math>\text{cm}^2</math> and perimeter <math>P</math> <math>\text{cm}</math>. Which of the following numbers cannot equal <math>A+P</math>?<br />
<br />
<math> \textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108 </math><br />
<br />
NOTE: As it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable.<br />
<br />
[[2015 AMC 10A Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
Tetrahedron <math>ABCD</math> has <math>AB=5</math>, <math>AC=3</math>, <math>BC=4</math>, <math>BD=4</math>, <math>AD=3</math>, and <math>CD=\tfrac{12}5\sqrt2</math>. What is the volume of the tetrahedron?<br />
<br />
<math>\textbf{(A) }3\sqrt2\qquad\textbf{(B) }2\sqrt5\qquad\textbf{(C) }\dfrac{24}5\qquad\textbf{(D) }3\sqrt3\qquad\textbf{(E) }\dfrac{24}5\sqrt2</math><br />
<br />
[[2015 AMC 10A Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
<br />
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?<br />
<br />
<math>\textbf{(A)}\dfrac{47}{256}\qquad\textbf{(B)}\dfrac{3}{16}\qquad\textbf{(C) }\dfrac{49}{256}\qquad\textbf{(D) }\dfrac{25}{128}\qquad\textbf{(E) }\dfrac{51}{256} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
<br />
The zeroes of the function <math>f(x)=x^2-ax+2a</math> are integers. What is the sum of the possible values of <math>a</math>?<br />
<br />
<math> \textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }16\qquad\textbf{(D) }17\qquad\textbf{(E) }18</math><br />
<br />
[[2015 AMC 10A Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
For some positive integers <math>p</math>, there is a quadrilateral <math>ABCD</math> with positive integer side lengths, perimeter <math>p</math>, right angles at <math>B</math> and <math>C</math>, <math>AB=2</math>, and <math>CD=AD</math>. How many different values of <math>p<2015</math> are possible?<br />
<br />
<math>\textbf{(A) }30\qquad\textbf{(B) }31\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
Let <math>S</math> be a square of side length <math>1</math>. Two points are chosen independently at random on the sides of <math>S</math>. The probability that the straight-line distance between the points is at least <math>\tfrac12</math> is <math>\tfrac{a-b\pi}c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers with <math>\gcd(a,b,c)=1</math>. What is <math>a+b+c</math>?<br />
<br />
<math>\textbf{(A) }59\qquad\textbf{(B) }60\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 25|Solution]]<br />
<br />
==See also==<br />
{{AMC10 box|year=2015|ab=A|before=[[2014 AMC 10B Problems]]|after=[[2015 AMC 10B Problems]]}}<br />
* [[AMC 10]]<br />
* [[AMC 10 Problems and Solutions]]<br />
* [[2015 AMC 10A]]<br />
* [[Mathematics competition resources]]<br />
{{MAA Notice}}</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2015_AMC_10A_Problems&diff=714422015 AMC 10A Problems2015-08-03T19:31:43Z<p>Doitsudoitsu: </p>
<hr />
<div>==Problem 1==<br />
<br />
What is the value of <math>(2^0-1+5^2-0)^{-1}\times5?</math><br />
<br />
<math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{5}{24}\qquad\textbf{(E)}\ 25</math><br />
<br />
[[2015 AMC 10A Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
<br />
A box contains a collection of triangular and square tiles. There are <math>25</math> tiles in the box, containing <math>84</math> edges total. How many square tiles are there in the box?<br />
<br />
<math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11</math><br />
<br />
[[2015 AMC 10A Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?<br />
<br />
[asy] size(150); defaultpen(linewidth(0.8)); path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); for(int i=0;i<=2;i=i+1) { for(int j=0;j<=3-i;j=j+1) { filldraw(shift((i,j))*h,black); filldraw(shift((j,i))*v,black); } }[/asy]<br />
<br />
<math>\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24</math><br />
<br />
[[2015 AMC 10A Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
<br />
Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?<br />
<br />
<math> \textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Mr. Patrick teaches math to <math> 15 </math> students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was <math> 80 </math>. After he graded Payton's test, the test average became <math> 81 </math>. What was Payton's score on the test?<br />
<br />
<math> \textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}\ 94\qquad\textbf{(E)}\ 95 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
<br />
The sum of two positive numbers is <math> 5 </math> times their difference. What is the ratio of the larger number to the smaller number?<br />
<br />
<math> \textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}\ 2 \qquad\textbf{(E)}\ \frac{5}{2} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
<br />
How many terms are there in the arithmetic sequence <math>13</math>, <math>16</math>, <math>19</math>, . . ., <math>70</math>, <math>73</math>?<br />
<br />
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 21\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 60\qquad\textbf{(E)}\ 61 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be <math>2</math> : <math>1</math>?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 8 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
Two right circular cylinders have the same volume. The radius of the second cylinder is <math>10\%</math> more than the radius of the first. What is the relationship between the heights of the two cylinders?<br />
<br />
<math>\textbf{(A)}\ \text{The second height is } 10\% \text{ less than the first.} \\ \textbf{(B)}\ \text{The first height is } 10\% \text{ more than the second.}\\ \textbf{(C)}\ \text{The second height is } 21\% \text{ less than the first.} \\ \textbf{(D)}\ \text{The first height is } 21\% \text{ more than the second.}\\ \textbf{(E)}\ \text{The second height is } 80\% \text{ of the first.}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
<br />
How many rearrangements of <math>abcd</math> are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either <math>ab</math> or <math>ba</math>.<br />
<br />
<math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4</math><br />
<br />
[[2015 AMC 10A Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
<br />
The ratio of the length to the width of a rectangle is <math>4</math> : <math>3</math>. If the rectangle has diagonal of length <math>d</math>, then the area may be expressed as <math>kd^2</math> for some constant <math>k</math>. What is <math>k</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{2}{7}\qquad\textbf{(B)}\ \frac{3}{7}\qquad\textbf{(C)}\ \frac{12}{25}\qquad\textbf{(D)}\ \frac{16}{25}\qquad\textbf{(E)}\ \frac{3}{4}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Points <math>(\sqrt{\pi}, a)</math> and <math>(\sqrt{\pi}, b)</math> are distinct points on the graph of <math>y^2+x^4=2x^2y+1</math>. What is <math>|a-b|</math>?<br />
<br />
<math> \textbf{(A) }1\qquad\textbf{(B) }\dfrac{\pi}{2}\qquad\textbf{(C) }2\qquad\textbf{(D) }\sqrt{1+\pi}\qquad\textbf{(E) }1+\sqrt{\pi} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?<br />
<br />
<math> \textbf{(A) }3\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
<br />
The diagram below shows the circular face of a clock with radius <math>20</math> cm and a circular disk with radius <math>10</math> cm externally tangent to the clock face at <math>12</math> o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?<br />
<br />
<asy><br />
size(170);<br />
defaultpen(linewidth(0.9)+fontsize(13pt));<br />
draw(unitcircle^^circle((0,1.5),0.5));<br />
path arrow = origin--(-0.13,-0.35)--(-0.06,-0.35)--(-0.06,-0.7)--(0.06,-0.7)--(0.06,-0.35)--(0.13,-0.35)--cycle;<br />
for(int i=1;i<=12;i=i+1)<br />
{<br />
draw(0.9*dir(90-30*i)--dir(90-30*i));<br />
label("$"+(string) i+"$",0.78*dir(90-30*i));<br />
}<br />
dot(origin);<br />
draw(shift((0,1.87))*arrow);<br />
draw(arc(origin,1.5,68,30),EndArrow(size=12));<br />
</asy><br />
<br />
<math> \textbf{(A) }\mathrm{2 o'clock} \qquad\textbf{(B) }\mathrm{3 o'clock} \qquad\textbf{(C) }\mathrm{4 o'clock} \qquad\textbf{(D) }\mathrm{6 o'clock} \qquad\textbf{(E) }\mathrm{8 o'clock} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
Consider the set of all fractions <math>\tfrac{x}{y},</math> where <math>x</math> and <math>y</math> are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by <math>1</math>, the value of the fraction is increased by <math>10\%</math>?<br />
<br />
<math> \textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
If <math>y+4 = (x-2)^2, x+4 = (y-2)^2</math>, and <math>x \neq y</math>, what is the value of <math>x^2+y^2</math>?<br />
<br />
<math> \textbf{(A) }10\qquad\textbf{(B) }15\qquad\textbf{(C) }20\qquad\textbf{(D) }25\qquad\textbf{(E) }\text{30} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
A line that passes through the origin intersects both the line <math>x=1</math> and the line <math>y=1+\frac{\sqrt{3}}{3}x</math>. The three lines create an equilateral triangle. What is the perimeter of the triangle?<br />
<br />
<math> \textbf{(A) }2\sqrt{6}\qquad\textbf{(B) }2+2\sqrt{3}\qquad\textbf{(C) }6\qquad\textbf{(D) }3+2\sqrt{3}\qquad\textbf{(E) }6+\frac{\sqrt{3}}{3} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
Hexadecimal (base-16) numbers are written using numeric digits <math>0</math> through <math>9</math> as well as the letters <math>A</math> through <math>F</math> to represent <math>10</math> through <math>15</math>. Among the first <math>1000</math> positive integers, there are <math>n</math> whose hexadecimal representation contains only numeric digits. What is the sum of the digits of <math>n</math>?<br />
<br />
<math> \textbf{(A) }17\qquad\textbf{(B) }18\qquad\textbf{(C) }19\qquad\textbf{(D) }20\qquad\textbf{(E) }21 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
The isosceles right triangle <math>ABC</math> has right angle at <math>C</math> and area <math>12.5</math>. The rays trisecting <math>\angle ACB</math> intersect <math>AB</math> at <math>D</math> and <math>E</math>. What is the area of <math>\bigtriangleup CDE</math>?<br />
<br />
<math> \textbf{(A) }\dfrac{5\sqrt{2}}{3}\qquad\textbf{(B) }\dfrac{50\sqrt{3}-75}{4}\qquad\textbf{(C) }\dfrac{15\sqrt{3}}{8}\qquad\textbf{(D) }\dfrac{50-25\sqrt{3}}{2}\qquad\textbf{(E) }\dfrac{25}{6} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
<br />
A rectangle with positive integer side lengths in <math>\text{cm}</math> has area <math>A</math> <math>\text{cm}^2</math> and perimeter <math>P</math> <math>\text{cm}</math>. Which of the following numbers cannot equal <math>A+P</math>?<br />
<br />
<math> \textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108 </math><br />
<br />
NOTE: As it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable.<br />
<br />
[[2015 AMC 10A Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
Tetrahedron <math>ABCD</math> has <math>AB=5</math>, <math>AC=3</math>, <math>BC=4</math>, <math>BD=4</math>, <math>AD=3</math>, and <math>CD=\tfrac{12}5\sqrt2</math>. What is the volume of the tetrahedron?<br />
<br />
<math>\textbf{(A) }3\sqrt2\qquad\textbf{(B) }2\sqrt5\qquad\textbf{(C) }\dfrac{24}5\qquad\textbf{(D) }3\sqrt3\qquad\textbf{(E) }\dfrac{24}5\sqrt2</math><br />
<br />
[[2015 AMC 10A Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
<br />
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?<br />
<br />
<math>\textbf{(A)}\dfrac{47}{256}\qquad\textbf{(B)}\dfrac{3}{16}\qquad\textbf{(C) }\dfrac{49}{256}\qquad\textbf{(D) }\dfrac{25}{128}\qquad\textbf{(E) }\dfrac{51}{256} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
<br />
The zeroes of the function <math>f(x)=x^2-ax+2a</math> are integers. What is the sum of the possible values of <math>a</math>?<br />
<br />
<math> \textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }16\qquad\textbf{(D) }17\qquad\textbf{(E) }18</math><br />
<br />
[[2015 AMC 10A Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
For some positive integers <math>p</math>, there is a quadrilateral <math>ABCD</math> with positive integer side lengths, perimeter <math>p</math>, right angles at <math>B</math> and <math>C</math>, <math>AB=2</math>, and <math>CD=AD</math>. How many different values of <math>p<2015</math> are possible?<br />
<br />
<math>\textbf{(A) }30\qquad\textbf{(B) }31\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
Let <math>S</math> be a square of side length <math>1</math>. Two points are chosen independently at random on the sides of <math>S</math>. The probability that the straight-line distance between the points is at least <math>\tfrac12</math> is <math>\tfrac{a-b\pi}c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers with <math>\gcd(a,b,c)=1</math>. What is <math>a+b+c</math>?<br />
<br />
<math>\textbf{(A) }59\qquad\textbf{(B) }60\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 25|Solution]]<br />
<br />
==See also==<br />
{{AMC10 box|year=2015|ab=A|before=[[2014 AMC 10B Problems]]|after=[[2015 AMC 10B Problems]]}}<br />
* [[AMC 10]]<br />
* [[AMC 10 Problems and Solutions]]<br />
* [[2015 AMC 10A]]<br />
* [[Mathematics competition resources]]<br />
{{MAA Notice}}</div>Doitsudoitsuhttps://artofproblemsolving.com/wiki/index.php?title=2015_AMC_10A_Problems&diff=714412015 AMC 10A Problems2015-08-03T19:31:20Z<p>Doitsudoitsu: add diagram</p>
<hr />
<div>==Problem 1==<br />
<br />
What is the value of <math>(2^0-1+5^2-0)^{-1}\times5?</math><br />
<br />
<math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{5}{24}\qquad\textbf{(E)}\ 25</math><br />
<br />
[[2015 AMC 10A Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
<br />
A box contains a collection of triangular and square tiles. There are <math>25</math> tiles in the box, containing <math>84</math> edges total. How many square tiles are there in the box?<br />
<br />
<math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11</math><br />
<br />
[[2015 AMC 10A Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?<br />
<br />
[asy] size(50); defaultpen(linewidth(0.8)); path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); for(int i=0;i<=2;i=i+1) { for(int j=0;j<=3-i;j=j+1) { filldraw(shift((i,j))*h,black); filldraw(shift((j,i))*v,black); } }[/asy]<br />
<br />
<math>\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24</math><br />
<br />
[[2015 AMC 10A Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
<br />
Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?<br />
<br />
<math> \textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Mr. Patrick teaches math to <math> 15 </math> students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was <math> 80 </math>. After he graded Payton's test, the test average became <math> 81 </math>. What was Payton's score on the test?<br />
<br />
<math> \textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}\ 94\qquad\textbf{(E)}\ 95 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
<br />
The sum of two positive numbers is <math> 5 </math> times their difference. What is the ratio of the larger number to the smaller number?<br />
<br />
<math> \textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}\ 2 \qquad\textbf{(E)}\ \frac{5}{2} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
<br />
How many terms are there in the arithmetic sequence <math>13</math>, <math>16</math>, <math>19</math>, . . ., <math>70</math>, <math>73</math>?<br />
<br />
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 21\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 60\qquad\textbf{(E)}\ 61 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be <math>2</math> : <math>1</math>?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 8 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
Two right circular cylinders have the same volume. The radius of the second cylinder is <math>10\%</math> more than the radius of the first. What is the relationship between the heights of the two cylinders?<br />
<br />
<math>\textbf{(A)}\ \text{The second height is } 10\% \text{ less than the first.} \\ \textbf{(B)}\ \text{The first height is } 10\% \text{ more than the second.}\\ \textbf{(C)}\ \text{The second height is } 21\% \text{ less than the first.} \\ \textbf{(D)}\ \text{The first height is } 21\% \text{ more than the second.}\\ \textbf{(E)}\ \text{The second height is } 80\% \text{ of the first.}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
<br />
How many rearrangements of <math>abcd</math> are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either <math>ab</math> or <math>ba</math>.<br />
<br />
<math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4</math><br />
<br />
[[2015 AMC 10A Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
<br />
The ratio of the length to the width of a rectangle is <math>4</math> : <math>3</math>. If the rectangle has diagonal of length <math>d</math>, then the area may be expressed as <math>kd^2</math> for some constant <math>k</math>. What is <math>k</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{2}{7}\qquad\textbf{(B)}\ \frac{3}{7}\qquad\textbf{(C)}\ \frac{12}{25}\qquad\textbf{(D)}\ \frac{16}{25}\qquad\textbf{(E)}\ \frac{3}{4}</math><br />
<br />
[[2015 AMC 10A Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Points <math>(\sqrt{\pi}, a)</math> and <math>(\sqrt{\pi}, b)</math> are distinct points on the graph of <math>y^2+x^4=2x^2y+1</math>. What is <math>|a-b|</math>?<br />
<br />
<math> \textbf{(A) }1\qquad\textbf{(B) }\dfrac{\pi}{2}\qquad\textbf{(C) }2\qquad\textbf{(D) }\sqrt{1+\pi}\qquad\textbf{(E) }1+\sqrt{\pi} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?<br />
<br />
<math> \textbf{(A) }3\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
<br />
The diagram below shows the circular face of a clock with radius <math>20</math> cm and a circular disk with radius <math>10</math> cm externally tangent to the clock face at <math>12</math> o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?<br />
<br />
<asy><br />
size(170);<br />
defaultpen(linewidth(0.9)+fontsize(13pt));<br />
draw(unitcircle^^circle((0,1.5),0.5));<br />
path arrow = origin--(-0.13,-0.35)--(-0.06,-0.35)--(-0.06,-0.7)--(0.06,-0.7)--(0.06,-0.35)--(0.13,-0.35)--cycle;<br />
for(int i=1;i<=12;i=i+1)<br />
{<br />
draw(0.9*dir(90-30*i)--dir(90-30*i));<br />
label("$"+(string) i+"$",0.78*dir(90-30*i));<br />
}<br />
dot(origin);<br />
draw(shift((0,1.87))*arrow);<br />
draw(arc(origin,1.5,68,30),EndArrow(size=12));<br />
</asy><br />
<br />
<math> \textbf{(A) }\mathrm{2 o'clock} \qquad\textbf{(B) }\mathrm{3 o'clock} \qquad\textbf{(C) }\mathrm{4 o'clock} \qquad\textbf{(D) }\mathrm{6 o'clock} \qquad\textbf{(E) }\mathrm{8 o'clock} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
Consider the set of all fractions <math>\tfrac{x}{y},</math> where <math>x</math> and <math>y</math> are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by <math>1</math>, the value of the fraction is increased by <math>10\%</math>?<br />
<br />
<math> \textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
If <math>y+4 = (x-2)^2, x+4 = (y-2)^2</math>, and <math>x \neq y</math>, what is the value of <math>x^2+y^2</math>?<br />
<br />
<math> \textbf{(A) }10\qquad\textbf{(B) }15\qquad\textbf{(C) }20\qquad\textbf{(D) }25\qquad\textbf{(E) }\text{30} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
A line that passes through the origin intersects both the line <math>x=1</math> and the line <math>y=1+\frac{\sqrt{3}}{3}x</math>. The three lines create an equilateral triangle. What is the perimeter of the triangle?<br />
<br />
<math> \textbf{(A) }2\sqrt{6}\qquad\textbf{(B) }2+2\sqrt{3}\qquad\textbf{(C) }6\qquad\textbf{(D) }3+2\sqrt{3}\qquad\textbf{(E) }6+\frac{\sqrt{3}}{3} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
Hexadecimal (base-16) numbers are written using numeric digits <math>0</math> through <math>9</math> as well as the letters <math>A</math> through <math>F</math> to represent <math>10</math> through <math>15</math>. Among the first <math>1000</math> positive integers, there are <math>n</math> whose hexadecimal representation contains only numeric digits. What is the sum of the digits of <math>n</math>?<br />
<br />
<math> \textbf{(A) }17\qquad\textbf{(B) }18\qquad\textbf{(C) }19\qquad\textbf{(D) }20\qquad\textbf{(E) }21 </math><br />
<br />
[[2015 AMC 10A Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
The isosceles right triangle <math>ABC</math> has right angle at <math>C</math> and area <math>12.5</math>. The rays trisecting <math>\angle ACB</math> intersect <math>AB</math> at <math>D</math> and <math>E</math>. What is the area of <math>\bigtriangleup CDE</math>?<br />
<br />
<math> \textbf{(A) }\dfrac{5\sqrt{2}}{3}\qquad\textbf{(B) }\dfrac{50\sqrt{3}-75}{4}\qquad\textbf{(C) }\dfrac{15\sqrt{3}}{8}\qquad\textbf{(D) }\dfrac{50-25\sqrt{3}}{2}\qquad\textbf{(E) }\dfrac{25}{6} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
<br />
A rectangle with positive integer side lengths in <math>\text{cm}</math> has area <math>A</math> <math>\text{cm}^2</math> and perimeter <math>P</math> <math>\text{cm}</math>. Which of the following numbers cannot equal <math>A+P</math>?<br />
<br />
<math> \textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108 </math><br />
<br />
NOTE: As it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable.<br />
<br />
[[2015 AMC 10A Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
Tetrahedron <math>ABCD</math> has <math>AB=5</math>, <math>AC=3</math>, <math>BC=4</math>, <math>BD=4</math>, <math>AD=3</math>, and <math>CD=\tfrac{12}5\sqrt2</math>. What is the volume of the tetrahedron?<br />
<br />
<math>\textbf{(A) }3\sqrt2\qquad\textbf{(B) }2\sqrt5\qquad\textbf{(C) }\dfrac{24}5\qquad\textbf{(D) }3\sqrt3\qquad\textbf{(E) }\dfrac{24}5\sqrt2</math><br />
<br />
[[2015 AMC 10A Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
<br />
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?<br />
<br />
<math>\textbf{(A)}\dfrac{47}{256}\qquad\textbf{(B)}\dfrac{3}{16}\qquad\textbf{(C) }\dfrac{49}{256}\qquad\textbf{(D) }\dfrac{25}{128}\qquad\textbf{(E) }\dfrac{51}{256} </math><br />
<br />
[[2015 AMC 10A Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
<br />
The zeroes of the function <math>f(x)=x^2-ax+2a</math> are integers. What is the sum of the possible values of <math>a</math>?<br />
<br />
<math> \textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }16\qquad\textbf{(D) }17\qquad\textbf{(E) }18</math><br />
<br />
[[2015 AMC 10A Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
For some positive integers <math>p</math>, there is a quadrilateral <math>ABCD</math> with positive integer side lengths, perimeter <math>p</math>, right angles at <math>B</math> and <math>C</math>, <math>AB=2</math>, and <math>CD=AD</math>. How many different values of <math>p<2015</math> are possible?<br />
<br />
<math>\textbf{(A) }30\qquad\textbf{(B) }31\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
Let <math>S</math> be a square of side length <math>1</math>. Two points are chosen independently at random on the sides of <math>S</math>. The probability that the straight-line distance between the points is at least <math>\tfrac12</math> is <math>\tfrac{a-b\pi}c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers with <math>\gcd(a,b,c)=1</math>. What is <math>a+b+c</math>?<br />
<br />
<math>\textbf{(A) }59\qquad\textbf{(B) }60\qquad\textbf{(C) }61\qquad\textbf{(D) }62\qquad\textbf{(E) }63</math><br />
<br />
[[2015 AMC 10A Problems/Problem 25|Solution]]<br />
<br />
==See also==<br />
{{AMC10 box|year=2015|ab=A|before=[[2014 AMC 10B Problems]]|after=[[2015 AMC 10B Problems]]}}<br />
* [[AMC 10]]<br />
* [[AMC 10 Problems and Solutions]]<br />
* [[2015 AMC 10A]]<br />
* [[Mathematics competition resources]]<br />
{{MAA Notice}}</div>Doitsudoitsu