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Difference between revisions of "User:Cxsmi"

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==Welcome==
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Welcome to my user page! Here, I compile lists of solutions I write on this wiki and post original problems I come up with for the world to see. Please add one to the visit count below if this is your first time on my user page (I got the idea from [https://artofproblemsolving.com/wiki/index.php/User:MRENTHUSIASM MRENTHUSIASM]). Thanks for visiting my user page, and enjoy your stay!
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 +
==Visit Count==
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</font></div><center><font size="100px">6</font></center>
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==About Me==
 
==About Me==
−
Hi! I'm just another guy who happens to enjoy math. I often pop onto the AOPS wiki and look for problems to solve, and I sometimes even write solutions for them! I've starred ⭐ a few of my favorite solutions below; please feel free to take a look at any of them. Thanks for visiting my user page, and enjoy your stay!
+
Hi! I'm just another guy who happens to enjoy math. I often pop onto the AOPS wiki and look for problems to solve, and I sometimes even write solutions for them! I've starred ⭐ a few of my favorite solutions below; please feel free to take a look at any of them.
  
 
==Solutions==
 
==Solutions==
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# [https://artofproblemsolving.com/wiki/index.php?title=1987_AIME_Problems/Problem_11#Solution_3 1987 AIME Problem 11 Solution 3 ⭐]
 
# [https://artofproblemsolving.com/wiki/index.php?title=1987_AIME_Problems/Problem_11#Solution_3 1987 AIME Problem 11 Solution 3 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2012_AIME_I_Problems/Problem_2#Solution_3 2012 AIME I Problem 2 Solution 3 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2012_AIME_I_Problems/Problem_2#Solution_3 2012 AIME I Problem 2 Solution 3]
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# [https://artofproblemsolving.com/wiki/index.php/2024_AIME_I_Problems/Problem_6#Solution_5 2024 AIME I Problem 6 Solution 5]
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# [https://artofproblemsolving.com/wiki/index.php/2000_AIME_II_Problems/Problem_1#Solution_4 2000 AIME II Problem 1 Solution 4]
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# [https://artofproblemsolving.com/wiki/index.php/1985_AIME_Problems/Problem_12#Solution_9 1985 AIME Problem 12 Solution 9 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2012_AIME_I_Problems/Problem_8#Solution_7 2012 AIME I Problem 8 Solution 7]
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# [https://artofproblemsolving.com/wiki/index.php/1987_AIME_Problems/Problem_14#Solution_4 1987 AIME Problem 14 Solution 4]
  
 
===AMC 8===
 
===AMC 8===
  
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# [https://artofproblemsolving.com/wiki/index.php/2012_AMC_8_Problems/Problem_19#Solution_6 2012 AMC 8 Problem 19 Solution 6 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2012_AMC_8_Problems/Problem_19#Solution_6 2012 AMC 8 Problem 19 Solution 6]
 
# [https://artofproblemsolving.com/wiki/index.php/2002_AMC_8_Problems/Problem_17#Solution_3 2002 AMC 8 Problem 17 Solution 3]
 
# [https://artofproblemsolving.com/wiki/index.php/2002_AMC_8_Problems/Problem_17#Solution_3 2002 AMC 8 Problem 17 Solution 3]
 
# [https://artofproblemsolving.com/wiki/index.php/2007_AMC_8_Problems/Problem_20#Solution_8_.28Answer_Choices.29 2007 AMC 8 Problem 20 Solution 8]
 
# [https://artofproblemsolving.com/wiki/index.php/2007_AMC_8_Problems/Problem_20#Solution_8_.28Answer_Choices.29 2007 AMC 8 Problem 20 Solution 8]
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# [https://artofproblemsolving.com/wiki/index.php/2018_AMC_8_Problems/Problem_23#Solution_5 2018 AMC 8 Problem 23 Solution 5 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2018_AMC_8_Problems/Problem_23#Solution_5_.28Casework.29 2018 AMC 8 Problem 23 Solution 5 ⭐]
 
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_8_Problems/Problem_13#Solution_3_.28Casework.29 2016 AMC 8 Problem 13 Solution 3]
 
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_8_Problems/Problem_13#Solution_3_.28Casework.29 2016 AMC 8 Problem 13 Solution 3]
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_8_Problems/Problem_9#Solution_2 2017 AMC 8 Problem 9 Solution 2]
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_8_Problems/Problem_9#Solution_2 2017 AMC 8 Problem 9 Solution 2]
 
# [https://artofproblemsolving.com/wiki/index.php/2012_AMC_8_Problems/Problem_20#Solution_7 2012 AMC 8 Problem 20 Solution 7]
 
# [https://artofproblemsolving.com/wiki/index.php/2012_AMC_8_Problems/Problem_20#Solution_7 2012 AMC 8 Problem 20 Solution 7]
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# [https://artofproblemsolving.com/wiki/index.php/2010_AMC_8_Problems/Problem_25#Solution_3_.28Recursion.29 2010 AMC 8 Problem 25 Solution 3]
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# [https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_11#Solution_3 2024 AMC 8 Problem 11 Solution 3 ⭐]
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# [https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_18#Solution_4 2024 AMC 8 Problem 18 Solution 4]
 +
# [https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_11#Solution_4 2024 AMC 8 Problem 11 Solution 4]
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# [https://artofproblemsolving.com/wiki/index.php/2019_AMC_8_Problems/Problem_15#Solution_2 2019 AMC 8 Problem 15 Solution 2 ⭐]
  
 
===AJHSME===
 
===AJHSME===
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# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_40#Solution_2 1950 AHSME Problem 40 Solution 2]
 
# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_40#Solution_2 1950 AHSME Problem 40 Solution 2]
 
# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_41#Solution_2 1950 AHSME Problem 41 Solution 2]
 
# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_41#Solution_2 1950 AHSME Problem 41 Solution 2]
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# [https://artofproblemsolving.com/wiki/index.php/1972_AHSME_Problems/Problem_16#Solution_2 1972 AHSME Problem 16 Solution 2 ⭐]  
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# [https://artofproblemsolving.com/wiki/index.php/1972_AHSME_Problems/Problem_16#Solution_2 1972 AHSME Problem 16 Solution 2]  
 
# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_45#Solution_3 1950 AHSME Problem 45 Solution 3]
 
# [https://artofproblemsolving.com/wiki/index.php/1950_AHSME_Problems/Problem_45#Solution_3 1950 AHSME Problem 45 Solution 3]
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# [https://artofproblemsolving.com/wiki/index.php/1956_AHSME_Problems/Problem_23#Solution 1956 AHSME Problem 23 Solution 1]
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# [https://artofproblemsolving.com/wiki/index.php/1982_AHSME_Problems/Problem_13#Solution_2 1982 AHSME Problem 13 Solution 2]
  
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===AMC 12===
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===AMC 10/12===
  
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#[https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_12#Solution_6 2021 AMC 12B Problem 12 Solution 6⭐]
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#[https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_12#Solution_6 2021 Fall AMC 12B Problem 12 Solution 6]
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#[https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_1#Solution_4_.28Brute_Force.29 2021 Fall AMC 10B Problem 1/AMC 12B Problem 1 Solution 4]
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#[https://artofproblemsolving.com/wiki/index.php/2003_AMC_10A_Problems/Problem_17#Solution_2 2003 AMC 10A Problem 17 Solution 2]
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#[https://artofproblemsolving.com/wiki/index.php/2015_AMC_12B_Problems/Problem_8#Solution_3 2015 AMC 12B Problem 8 Solution 3]
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#[https://artofproblemsolving.com/wiki/index.php/2003_AMC_12B_Problems/Problem_17#Solution_4 2003 AMC 12B Problem 17 Solution 4]
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#[https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_18#Solution_6 2020 AMC 10A Problem 18 Solution 6]
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#[https://artofproblemsolving.com/wiki/index.php/2021_AMC_10B_Problems/Problem_13#Solution_4 2021 AMC 10B Problem 13 Solution 4]
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#[https://artofproblemsolving.com/wiki/index.php/2007_AMC_10B_Problems/Problem_23#Solution_4 2007 AMC 10B Problem 23 Solution 4]
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#[https://artofproblemsolving.com/wiki/index.php/2005_AMC_10A_Problems/Problem_24#Solution_3 2005 AMC 10B Problem 24 Solution 3 ⭐]
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#[https://artofproblemsolving.com/wiki/index.php/2008_AMC_12B_Problems/Problem_24#Solution_4_.28Pattern_Observation.29 2008 AMC 12B Problem 24 Solution 4 ⭐]
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#[https://artofproblemsolving.com/wiki/index.php/2023_AMC_10B_Problems/Problem_24#Solution_2 2023 AMC 10B Problem 24 Solution 2 ⭐]
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#[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_9#Solution_5_.28Desperate.29 2023 AMC 10B Problem 13/AMC 12B Problem 9 Solution 5]
  
 
==Significant Problems==
 
==Significant Problems==
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Here are some problems that, to me, have been significant on my math journey. This section is mainly for myself, but please please feel free to look at the problems if you're interested.
+
Here are some problems that, to me, have been significant on my math journey. This section is mainly for myself, but please please feel free to look at the problems if you're interested. Any referenced "difficulties" are from [https://artofproblemsolving.com/wiki/index.php/AoPS_Wiki:Competition_ratings this page].
  
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_10A_Problems/Problem_19 2017 AMC 10A Problem 19 - First AMC 10 Solution of Difficulty 2 or Higher]
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_10A_Problems/Problem_19 2017 AMC 10A Problem 19 - First AMC 10 Solution of Difficulty 2 or Higher]
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# [https://artofproblemsolving.com/wiki/index.php/2005_AMC_12B_Problems/Problem_16 2005 AMC 12B Problem 16 - First AMC 12 Solution of Difficulty 2.5 or Higher]
 
# [https://artofproblemsolving.com/wiki/index.php/2005_AMC_12B_Problems/Problem_16 2005 AMC 12B Problem 16 - First AMC 12 Solution of Difficulty 2.5 or Higher]
 
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_22 2016 AMC 10A Problem 21 - First AMC 10 Final Five Solution]
 
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_22 2016 AMC 10A Problem 21 - First AMC 10 Final Five Solution]
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# [https://artofproblemsolving.com/wiki/index.php/1987_AIME_Problems/Problem_11 1987 AIME Problem 11 - First AIME Solution of Difficulty 4 or Higher]
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# [https://artofproblemsolving.com/wiki/index.php/1987_AIME_Problems/Problem_11 1987 AIME Problem 11 - First AIME Solution of Difficulty 4 or Higher; First AIME Solution of Difficulty 5 or Higher]
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_12A_Problems/Problem_23 2017 AMC 12A Problem 23 - First AMC 12 Final Five Solution]
 
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_12A_Problems/Problem_23 2017 AMC 12A Problem 23 - First AMC 12 Final Five Solution]
 +
# [https://artofproblemsolving.com/wiki/index.php/2001_AIME_I_Problems/Problem_14 2001 AIME I Problem 14 - First AIME Solution of Difficulty 6 or Higher]
 +
 +
==Other Major Contributions==
 +
# [https://artofproblemsolving.com/wiki/index.php/Titu%27s_Lemma Titu's Lemma (all examples and problems)]
  
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==Problem==
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==Some Problems I Wrote==
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I enjoy writing problems when I see concepts that interest me. I've written a few of them below; please feel free to solve them! Note: Unless otherwise stated, all questions are in the AIME format -- that is, the answer is an integer between 1 and 999.
+
All problems and solutions have been moved to [https://www.dropbox.com/scl/fi/3ibl1exa0cyukba7e5si0/Problem_Collection-16.pdf?rlkey=379sf9mr6u5wxbfx4y0s1mvbv&st=8u5tq9ky&dl=0 this page].
  
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===Problem 1===
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Last Updated: Apr 27, 2024
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Find the least positive integer <math>n</math> that satisfies the following. The notation <math>\lfloor{x}\rfloor</math> represents the greatest integer less than or equal to <math>x</math>.
 
  
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<math>\frac{20^{23}}{n} + \frac{24^{23}}{n} = \lfloor{\frac{20^{23}}{n}+\frac{24^{23}}{n}}\rfloor \neq \lfloor{\frac{20^{23}}{n}}\rfloor + \lfloor{\frac{24^{23}}{n}}\rfloor</math>
 
  
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===Problem 2===
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If you find an issue or have an alternate solution, please feel free to put it below! I'll add it to the document.
−
Bob has received a test. He must match a list of <math>2024</math> words to a list of <math>2024</math> definitions such that each word matches with exactly one definition and vice versa. He does not know any of the words, so he will guess randomly. How many correct matches can he expect to make?
 

Revision as of 01:14, 13 May 2024

Welcome

Welcome to my user page! Here, I compile lists of solutions I write on this wiki and post original problems I come up with for the world to see. Please add one to the visit count below if this is your first time on my user page (I got the idea from MRENTHUSIASM). Thanks for visiting my user page, and enjoy your stay!

Visit Count

6

About Me

Hi! I'm just another guy who happens to enjoy math. I often pop onto the AOPS wiki and look for problems to solve, and I sometimes even write solutions for them! I've starred ⭐ a few of my favorite solutions below; please feel free to take a look at any of them.

Solutions

AIME

  1. 1987 AIME Problem 11 Solution 3 ⭐
  2. 2012 AIME I Problem 2 Solution 3
  3. 2024 AIME I Problem 6 Solution 5
  4. 2000 AIME II Problem 1 Solution 4
  5. 1985 AIME Problem 12 Solution 9 ⭐
  6. 2012 AIME I Problem 8 Solution 7
  7. 1987 AIME Problem 14 Solution 4

AMC 8

  1. 2012 AMC 8 Problem 19 Solution 6
  2. 2002 AMC 8 Problem 17 Solution 3
  3. 2007 AMC 8 Problem 20 Solution 8
  4. 2018 AMC 8 Problem 23 Solution 5 ⭐
  5. 2016 AMC 8 Problem 13 Solution 3
  6. 2017 AMC 8 Problem 9 Solution 2
  7. 2012 AMC 8 Problem 20 Solution 7
  8. 2010 AMC 8 Problem 25 Solution 3
  9. 2024 AMC 8 Problem 11 Solution 3 ⭐
  10. 2024 AMC 8 Problem 18 Solution 4
  11. 2024 AMC 8 Problem 11 Solution 4
  12. 2019 AMC 8 Problem 15 Solution 2 ⭐

AJHSME

  1. 1997 AJHSME Problem 22 Solution 1
  2. 1985 AJHSME Problem 1 Solution 2
  3. 1985 AJHSME Problem 24 Solution 2 ⭐
  4. 1985 AJHSME Problem 2 Solution 5

AHSME

  1. 1950 AHSME Problem 40 Solution 2
  2. 1950 AHSME Problem 41 Solution 2
  3. 1972 AHSME Problem 16 Solution 2
  4. 1950 AHSME Problem 45 Solution 3
  5. 1956 AHSME Problem 23 Solution 1
  6. 1982 AHSME Problem 13 Solution 2

AMC 10/12

  1. 2021 Fall AMC 12B Problem 12 Solution 6
  2. 2021 Fall AMC 10B Problem 1/AMC 12B Problem 1 Solution 4
  3. 2003 AMC 10A Problem 17 Solution 2
  4. 2015 AMC 12B Problem 8 Solution 3
  5. 2003 AMC 12B Problem 17 Solution 4
  6. 2020 AMC 10A Problem 18 Solution 6
  7. 2021 AMC 10B Problem 13 Solution 4
  8. 2007 AMC 10B Problem 23 Solution 4
  9. 2005 AMC 10B Problem 24 Solution 3 ⭐
  10. 2008 AMC 12B Problem 24 Solution 4 ⭐
  11. 2023 AMC 10B Problem 24 Solution 2 ⭐
  12. 2023 AMC 10B Problem 13/AMC 12B Problem 9 Solution 5

Significant Problems

Here are some problems that, to me, have been significant on my math journey. This section is mainly for myself, but please please feel free to look at the problems if you're interested. Any referenced "difficulties" are from this page.

  1. 2017 AMC 10A Problem 19 - First AMC 10 Solution of Difficulty 2 or Higher
  2. 2007 AMC 8 Problem 25 - First AMC 8 Final Five Solution
  3. 1984 AIME Problem 1 - First AIME Solution
  4. 2005 AMC 12B Problem 16 - First AMC 12 Solution of Difficulty 2.5 or Higher
  5. 2016 AMC 10A Problem 21 - First AMC 10 Final Five Solution
  6. 1987 AIME Problem 11 - First AIME Solution of Difficulty 4 or Higher; First AIME Solution of Difficulty 5 or Higher
  7. 2017 AMC 12A Problem 23 - First AMC 12 Final Five Solution
  8. 2001 AIME I Problem 14 - First AIME Solution of Difficulty 6 or Higher

Other Major Contributions

  1. Titu's Lemma (all examples and problems)

Some Problems I Wrote

All problems and solutions have been moved to this page.

Last Updated: Apr 27, 2024


If you find an issue or have an alternate solution, please feel free to put it below! I'll add it to the document.

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