https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Beautifulmath&feedformat=atomAoPS Wiki - User contributions [en]2024-03-28T12:48:21ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=User:MRENTHUSIASM&diff=162810User:MRENTHUSIASM2021-09-27T20:44:11Z<p>Beautifulmath: /* User Count */</p>
<hr />
<div>==User Count==<br />
If this is your first time visiting this page, then edit it by incrementing the user count below by one.</font></div><br />
<center><font size="100px">60</font></center><br />
<br />
==Introduction==<br />
Hi Everyone,<br />
<br />
I am a hedgehog who likes Message Board halping, funny pictures, emoji wars, and AoPS Wiki contributions. Keep these fun things coming!<br />
<br />
This hedgehog represents my attitude towards mathematics--victorious and enthusiastic!<br />
[[File:Victorious-Hedgehog.png|center]]<br />
And here is my personified self-portrait:<br />
[[File:Enthusiastic.gif|center]]<br />
~MRENTHUSIASM<br />
<br />
==AoPS Bio==<br />
Jerry graduated from Northeastern University in 2018 as a mathematics and computer science combined major. He has ten years of experience working with students. During his last two years in high school, he served as the math club president and prepared lively lectures on contest math. As a result, he inspired many kids to get interested in math and participate in math competitions (such as AMC and ARML). For the last eight years, he has worked with Math League to write math contests for students from grades 4 through 12 in the USA. Starting in 2019, he has served as an instructor and a Message Board Halper for many AoPS online classes and truly enjoyed that experience! In his mind, nothing is more rewarding than educating tomorrow’s bright minds. In his spare time, he loves contributing to the AoPS Wiki and playing chess and all sorts of board games, especially Scotland Yard and Samurai.<br />
<br />
==AoPS Wiki Contributions==<br />
Below are my contributions to the AMC/AIME Problems' Solutions in the AoPS Wiki. I understand that in this communal Wiki, we all have to collaborate and make compromises. <i><b>In any of my solutions, if you find flaws and/or want major revisions, then please contact me via my [[User_talk:MRENTHUSIASM|user talk page]] or the private messaging system before you take action. I am sure that we can work things out.</b></i><br />
<br />
Thank you for your cooperation, and hope you enjoy reading my solutions. :)<br />
<br />
~MRENTHUSIASM<br />
<br />
===AJHSME / AMC 8===<br />
* [[2007_AMC_8_Problems/Problem_8|2007 AMC 8 Problem 8]] (Solutions 1, 2)<br />
* [[2007_AMC_8_Problems/Problem_10|2007 AMC 8 Problem 10]] (Solution)<br />
* [[2009_AMC_8_Problems/Problem_4|2009 AMC 8 Problem 4]] (Solution)<br />
* [[2017_AMC_8_Problems/Problem_24|2017 AMC 8 Problem 24]] (Solution 1)<br />
* [[2020_AMC_8_Problems/Problem_1|2020 AMC 8 Problem 1]] (Solutions 2, 3)<br />
* [[2020_AMC_8_Problems/Problem_3|2020 AMC 8 Problem 3]] (Solution 3)<br />
* [[2020_AMC_8_Problems/Problem_4|2020 AMC 8 Problem 4]] (Solutions 3, 5)<br />
<br />
===AMC 10===<br />
* [[2004_AMC_10A_Problems/Problem_24|2004 AMC 10A Problem 24]] (Solutions 1, 2)<br />
* [[2007_AMC_10A_Problems/Problem_20|2007 AMC 10A Problem 20]] (Solutions 1, 2, 3, 4, 5, 6, 7)<br />
* [[2009_AMC_10B_Problems/Problem_1|2009 AMC 10B Problem 1]] (Solutions 1, 2, 3)<br />
* [[2012_AMC_10B_Problems/Problem_10|2012 AMC 10B Problem 10]] (Solutions 1, 2)<br />
* [[2018_AMC_10A_Problems/Problem_1|2018 AMC 10A Problem 1]] (Solution)<br />
* [[2018_AMC_10A_Problems/Problem_5|2018 AMC 10A Problem 5]] (Solution 3)<br />
* [[2018_AMC_10A_Problems/Problem_7|2018 AMC 10A Problem 7]] (Solution 1)<br />
* [[2018_AMC_10A_Problems/Problem_8|2018 AMC 10A Problem 8]] (Solution 3)<br />
* [[2018_AMC_10A_Problems/Problem_17|2018 AMC 10A Problem 17]] (Solution 4)<br />
* [[2018_AMC_10A_Problems/Problem_21|2018 AMC 10A Problem 21]] (Remark)<br />
* [[2018_AMC_10A_Problems/Problem_23|2018 AMC 10A Problem 23]] (Solution 1)<br />
* [[2018_AMC_10A_Problems/Problem_25|2018 AMC 10A Problem 25]] (Solutions 1, 3)<br />
* [[2018_AMC_10B_Problems/Problem_2|2018 AMC 10B Problem 2]] (Solutions 1, 2)<br />
* [[2018_AMC_10B_Problems/Problem_15|2018 AMC 10B Problem 15]] (Solutions 1, 3)<br />
* [[2018_AMC_10B_Problems/Problem_19|2018 AMC 10B Problem 19]] (Solution 1)<br />
* [[2018_AMC_10B_Problems/Problem_20|2018 AMC 10B Problem 20]] (Solutions 1, 2)<br />
* [[2020_AMC_10A_Problems/Problem_3|2020 AMC 10A Problem 3]] (Solutions 1, 3)<br />
* [[2020_AMC_10A_Problems/Problem_5|2020 AMC 10A Problem 5]] (Solution 3)<br />
* [[2020_AMC_10A_Problems/Problem_11|2020 AMC 10A Problem 11]] (Solution 5)<br />
* [[2020_AMC_10A_Problems/Problem_17|2020 AMC 10A Problem 17]] (Solution 1)<br />
* [[2020_AMC_10A_Problems/Problem_24|2020 AMC 10A Problem 24]] (Solution 11)<br />
* [[2020_AMC_10A_Problems/Problem_25|2020 AMC 10A Problem 25]] (Solution 2)<br />
* [[2020_AMC_10B_Problems/Problem_3|2020 AMC 10B Problem 3]] (Solution 1)<br />
* [[2020_AMC_10B_Problems/Problem_4|2020 AMC 10B Problem 4]] (Solution 3)<br />
* [[2020_AMC_10B_Problems/Problem_8|2020 AMC 10B Problem 8]] (Solution 4)<br />
* [[2020_AMC_10B_Problems/Problem_13|2020 AMC 10B Problem 13]] (Solution 1)<br />
* [[2020_AMC_10B_Problems/Problem_15|2020 AMC 10B Problem 15]] (Solutions 1, 3)<br />
* [[2020_AMC_10B_Problems/Problem_23|2020 AMC 10B Problem 23]] (Solution 1)<br />
* [[2021_AMC_10A_Problems/Problem_1|2021 AMC 10A Problem 1]] (Solution 2)<br />
* [[2021_AMC_10A_Problems/Problem_2|2021 AMC 10A Problem 2]] (Solutions 1, 2, 3, 4)<br />
* [[2021_AMC_10A_Problems/Problem_3|2021 AMC 10A Problem 3]] (Solution 3)<br />
* [[2021_AMC_10A_Problems/Problem_4|2021 AMC 10A Problem 4]] (Solutions 1, 3)<br />
* [[2021_AMC_10A_Problems/Problem_5|2021 AMC 10A Problem 5]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_10A_Problems/Problem_6|2021 AMC 10A Problem 6]] (Solutions 1, 2)<br />
* [[2021_AMC_10A_Problems/Problem_7|2021 AMC 10A Problem 7]] (Solutions 1, 3)<br />
* [[2021_AMC_10A_Problems/Problem_8|2021 AMC 10A Problem 8]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_10A_Problems/Problem_9|2021 AMC 10A Problem 9]] (Solution 2)<br />
* [[2021_AMC_10A_Problems/Problem_10|2021 AMC 10A Problem 10]] (Solution 7)<br />
* [[2021_AMC_10A_Problems/Problem_11|2021 AMC 10A Problem 11]] (Solutions 1, 3)<br />
* [[2021_AMC_10A_Problems/Problem_12|2021 AMC 10A Problem 12]] (Solution 1)<br />
* [[2021_AMC_10A_Problems/Problem_13|2021 AMC 10A Problem 13]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_10A_Problems/Problem_17|2021 AMC 10A Problem 17]] (Diagram, Solutions 1, 2)<br />
* [[2021_AMC_10A_Problems/Problem_18|2021 AMC 10A Problem 18]] (Solutions 1, 4)<br />
* [[2021_AMC_10A_Problems/Problem_20|2021 AMC 10A Problem 20]] (Solutions 2, 3)<br />
* [[2021_AMC_10A_Problems/Problem_21|2021 AMC 10A Problem 21]] (Diagram, Solution, Video Solution)<br />
* [[2021_AMC_10A_Problems/Problem_22|2021 AMC 10A Problem 22]] (Solution 2, Video Solution)<br />
* [[2021_AMC_10A_Problems/Problem_23|2021 AMC 10A Problem 23]] (Solution 3, Video Solution)<br />
* [[2021_AMC_10A_Problems/Problem_24|2021 AMC 10A Problem 24]] (Diagram, Solutions 1, 2, 3, Video Solution)<br />
* [[2021_AMC_10A_Problems/Problem_25|2021 AMC 10A Problem 25]] (Solutions 2, 3)<br />
* [[2021_AMC_10B_Problems/Problem_6|2021 AMC 10B Problem 6]] (Solution 3)<br />
* [[2021_AMC_10B_Problems/Problem_7|2021 AMC 10B Problem 7]] (Solution)<br />
* [[2021_AMC_10B_Problems/Problem_8|2021 AMC 10B Problem 8]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_10B_Problems/Problem_16|2021 AMC 10B Problem 16]] (Solution 4)<br />
* [[2021_AMC_10B_Problems/Problem_17|2021 AMC 10B Problem 17]] (Solution)<br />
* [[2021_AMC_10B_Problems/Problem_23|2021 AMC 10B Problem 23]] (Diagram)<br />
<br />
===AHSME / AMC 12===<br />
* [[1976_AHSME_Problems/Problem_24|1976 AHSME Problem 24]] (Solution)<br />
* [[1976_AHSME_Problems/Problem_25|1976 AHSME Problem 25]] (Solution)<br />
* [[1976_AHSME_Problems/Problem_27|1976 AHSME Problem 27]] (Solutions 1, 2)<br />
* [[1976_AHSME_Problems/Problem_28|1976 AHSME Problem 28]] (Solution)<br />
* [[1976_AHSME_Problems/Problem_30|1976 AHSME Problem 30]] (Solution)<br />
* [[1978_AHSME_Problems/Problem_20|1978 AHSME Problem 20]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_19|1982 AHSME Problem 19]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_21|1982 AHSME Problem 21]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_23|1982 AHSME Problem 23]] (Solutions 1, 2)<br />
* [[1982_AHSME_Problems/Problem_27|1982 AHSME Problem 27]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_28|1982 AHSME Problem 28]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_29|1982 AHSME Problem 29]] (Solution)<br />
* [[1982_AHSME_Problems/Problem_30|1982 AHSME Problem 30]] (Solution)<br />
* [[1990_AHSME_Problems/Problem_26|1990 AHSME Problem 26]] (Solutions 1, 2)<br />
* [[1991_AHSME_Problems/Problem_6|1991 AHSME Problem 6]] (Solution)<br />
* [[1991_AHSME_Problems/Problem_20|1991 AHSME Problem 20]] (Solution)<br />
* [[1991_AHSME_Problems/Problem_27|1991 AHSME Problem 27]] (Solution)<br />
* [[2004_AMC_12A_Problems/Problem_16|2004 AMC 12A Problem 16]] (Solution)<br />
* [[2004_AMC_12A_Problems/Problem_17|2004 AMC 12A Problem 17]]: same as [[2004_AMC_10A_Problems/Problem_24|2004 AMC 10A Problem 24]] (Solutions 1, 2)<br />
* [[2009_AMC_12B_Problems/Problem_1|2009 AMC 12B Problem 1]]: same as [[2009_AMC_10B_Problems/Problem_1|2009 AMC 10B Problem 1]] (Solutions 1, 2, 3)<br />
* [[2014_AMC_12A_Problems/Problem_18|2014 AMC 12A Problem 18]] (Solution 1)<br />
* [[2018_AMC_12A_Problems/Problem_2|2018 AMC 12A Problem 2]] (Solutions 1, 2)<br />
* [[2018_AMC_12A_Problems/Problem 4|2018 AMC 12A Problem 4]]: same as [[2018_AMC_10A_Problems/Problem_5|2018 AMC 10A Problem 5]] (Solution 3)<br />
* [[2018_AMC_12A_Problems/Problem_7|2018 AMC 12A Problem 7]]: same as [[2018_AMC_10A_Problems/Problem_7|2018 AMC 10A Problem 7]] (Solution 1)<br />
* [[2018_AMC_12A_Problems/Problem_12|2018 AMC 12A Problem 12]]: same as [[2018_AMC_10A_Problems/Problem_17|2018 AMC 10A Problem 17]] (Solution 4)<br />
* [[2018_AMC_12A_Problems/Problem_14|2018 AMC 12A Problem 14]] (Solutions 1, 2, 3, 4, 5)<br />
* [[2018_AMC_12A_Problems/Problem_16|2018 AMC 12A Problem 16]]: same as [[2018_AMC_10A_Problems/Problem_21|2018 AMC 10A Problem 21]] (Remark)<br />
* [[2018_AMC_12A_Problems/Problem_17|2018 AMC 12A Problem 17]]: same as [[2018_AMC_10A_Problems/Problem_23|2018 AMC 10A Problem 23]] (Solution 1)<br />
* [[2018_AMC_12A_Problems/Problem_19|2018 AMC 12A Problem 19]] (Solution 1)<br />
* [[2018_AMC_12A_Problems/Problem_21|2018 AMC 12A Problem 21]] (Solution 1)<br />
* [[2018_AMC_12A_Problems/Problem_22|2018 AMC 12A Problem 22]] (Solutions 1, 2, 3)<br />
* [[2018_AMC_12A_Problems/Problem_23|2018 AMC 12A Problem 23]] (Diagram, Solution 2)<br />
* [[2018_AMC_12A_Problems/Problem_24|2018 AMC 12A Problem 24]] (Solutions 1, 2, 3)<br />
* [[2018_AMC_12A_Problems/Problem_25|2018 AMC 12A Problem 25]]: same as [[2018_AMC_10A_Problems/Problem_25|2018 AMC 10A Problem 25]] (Solutions 1, 3)<br />
* [[2018_AMC_12B_Problems/Problem_2|2018 AMC 12B Problem 2]]: same as [[2018_AMC_10B_Problems/Problem_2|2018 AMC 10B Problem 2]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_4|2018 AMC 12B Problem 4]] (Solution)<br />
* [[2018_AMC_12B_Problems/Problem_6|2018 AMC 12B Problem 6]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_8|2018 AMC 12B Problem 8]] (Solution)<br />
* [[2018_AMC_12B_Problems/Problem_9|2018 AMC 12B Problem 9]] (Solutions 1, 2, 3, 4, 5, 6)<br />
* [[2018_AMC_12B_Problems/Problem_11|2018 AMC 12B Problem 11]]: same as [[2018_AMC_10B_Problems/Problem_15|2018 AMC 10B Problem 15]] (Solutions 1, 3)<br />
* [[2018_AMC_12B_Problems/Problem_12|2018 AMC 12B Problem 12]] (Solution)<br />
* [[2018_AMC_12B_Problems/Problem_13|2018 AMC 12B Problem 13]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_14|2018 AMC 12B Problem 14]]: same as [[2018_AMC_10B_Problems/Problem_19|2018 AMC 10B Problem 19]] (Solution 1)<br />
* [[2018_AMC_12B_Problems/Problem_18|2018 AMC 12B Problem 18]]: same as [[2018_AMC_10B_Problems/Problem_20|2018 AMC 10B Problem 20]] (Solutions 1, 2)<br />
* [[2020_AMC_12A_Problems/Problem_1|2020 AMC 12A Problem 1]] (Solution 3)<br />
* [[2020_AMC_12A_Problems/Problem_6|2020 AMC 12A Problem 6]] (Solution 2)<br />
* [[2020_AMC_12A_Problems/Problem_8|2020 AMC 12A Problem 8]]: same as [[2020_AMC_10A_Problems/Problem_11|2020 AMC 10A Problem 11]] (Solution 5)<br />
* [[2020_AMC_12A_Problems/Problem_9|2020 AMC 12A Problem 9]] (Solution)<br />
* [[2020_AMC_12A_Problems/Problem_10|2020 AMC 12A Problem 10]] (Solutions 1, 2, 5)<br />
* [[2020_AMC_12A_Problems/Problem_15|2020 AMC 12A Problem 15]] (Solutions 1, 2)<br />
* [[2020_AMC_12A_Problems/Problem_23|2020 AMC 12A Problem 23]]: same as [[2020_AMC_10A_Problems/Problem_25|2020 AMC 10A Problem 25]] (Solution 2)<br />
* [[2020_AMC_12A_Problems/Problem_25|2020 AMC 12A Problem 25]] (Solution 1, Remark)<br />
* [[2020_AMC_12B_Problems/Problem_3|2020 AMC 12B Problem 3]]: same as [[2020_AMC_10B_Problems/Problem_3|2020 AMC 10B Problem 3]] (Solution 1)<br />
* [[2020_AMC_12B_Problems/Problem_4|2020 AMC 12B Problem 4]]: same as [[2020_AMC_10B_Problems/Problem_4|2020 AMC 10B Problem 4]] (Solution 3)<br />
* [[2020_AMC_12B_Problems/Problem_5|2020 AMC 12B Problem 5]] (Solution 1)<br />
* [[2020_AMC_12B_Problems/Problem_6|2020 AMC 12B Problem 6]] (Solution 2)<br />
* [[2020_AMC_12B_Problems/Problem_10|2020 AMC 12B Problem 10]] (Diagram, Solution 7)<br />
* [[2020_AMC_12B_Problems/Problem_12|2020 AMC 12B Problem 12]] (Diagram)<br />
* [[2020_AMC_12B_Problems/Problem_13|2020 AMC 12B Problem 13]] (Solutions 1, 4)<br />
* [[2020_AMC_12B_Problems/Problem_19|2020 AMC 12B Problem 19]]: same as [[2020_AMC_10B_Problems/Problem_23|2020 AMC 10B Problem 23]] (Solution 1)<br />
* [[2021_AMC_12A_Problems/Problem_2|2021 AMC 12A Problem 2]] (Solutions 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_3|2021 AMC 12A Problem 3]]: same as [[2021_AMC_10A_Problems/Problem_3|2021 AMC 10A Problem 3]] (Solution 3)<br />
* [[2021_AMC_12A_Problems/Problem_4|2021 AMC 12A Problem 4]]: same as [[2021_AMC_10A_Problems/Problem_7|2021 AMC 10A Problem 7]] (Solutions 1, 3)<br />
* [[2021_AMC_12A_Problems/Problem_5|2021 AMC 12A Problem 5]]: same as [[2021_AMC_10A_Problems/Problem_8|2021 AMC 10A Problem 8]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_6|2021 AMC 12A Problem 6]] (Solutions 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_7|2021 AMC 12A Problem 7]]: same as [[2021_AMC_10A_Problems/Problem_9|2021 AMC 10A Problem 9]] (Solution 2)<br />
* [[2021_AMC_12A_Problems/Problem_9|2021 AMC 12A Problem 9]]: same as [[2021_AMC_10A_Problems/Problem_10|2021 AMC 10A Problem 10]] (Solution 7)<br />
* [[2021_AMC_12A_Problems/Problem_10|2021 AMC 12A Problem 10]]: same as [[2021_AMC_10A_Problems/Problem_12|2021 AMC 10A Problem 12]] (Solution 1)<br />
* [[2021_AMC_12A_Problems/Problem_11|2021 AMC 12A Problem 11]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_13|2021 AMC 12A Problem 13]] (Solutions 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_14|2021 AMC 12A Problem 14]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_15|2021 AMC 12A Problem 15]] (Solutions 1, 2, 4)<br />
* [[2021_AMC_12A_Problems/Problem_17|2021 AMC 12A Problem 17]]: same as [[2021_AMC_10A_Problems/Problem_17|2021 AMC 10A Problem 17]] (Diagram, Solutions 1, 2)<br />
* [[2021_AMC_12A_Problems/Problem_18|2021 AMC 12A Problem 18]]: same as [[2021_AMC_10A_Problems/Problem_18|2021 AMC 10A Problem 18]] (Solutions 1, 4)<br />
* [[2021_AMC_12A_Problems/Problem_19|2021 AMC 12A Problem 19]] (Solutions 1, 2, 3)<br />
* [[2021_AMC_12A_Problems/Problem_21|2021 AMC 12A Problem 21]] (Solution 2)<br />
* [[2021_AMC_12A_Problems/Problem_22|2021 AMC 12A Problem 22]] (Solutions 1, 2, 3, 4, 5)<br />
* [[2021_AMC_12A_Problems/Problem_23|2021 AMC 12A Problem 23]]: same as [[2021_AMC_10A_Problems/Problem_23|2021 AMC 10A Problem 23]] (Solution 3, Video Solution)<br />
* [[2021_AMC_12A_Problems/Problem_24|2021 AMC 12A Problem 24]] (Solution 1)<br />
* [[2021_AMC_12A_Problems/Problem_25|2021 AMC 12A Problem 25]] (Solution 1)<br />
* [[2021_AMC_12B_Problems/Problem_4|2021 AMC 12B Problem 4]]: same as [[2021_AMC_10B_Problems/Problem_6|2021 AMC 10B Problem 6]] (Solution 3)<br />
* [[2021_AMC_12B_Problems/Problem_11|2021 AMC 12B Problem 11]] (Solution 4)<br />
* [[2021_AMC_12B_Problems/Problem_14|2021 AMC 12B Problem 14]] (Solution 3)<br />
* [[2021_AMC_12B_Problems/Problem_20|2021 AMC 12B Problem 20]] (Solution 4)<br />
* [[2021_AMC_12B_Problems/Problem_21|2021 AMC 12B Problem 21]] (Solution 3)<br />
* [[2021_AMC_12B_Problems/Problem_23|2021 AMC 12B Problem 23]] (Solution 4)<br />
<br />
===AIME===<br />
* [[1984_AIME_Problems/Problem_4|1984 AIME Problem 4]] (Solutions 1, 2)<br />
* [[1984_AIME_Problems/Problem_10|1984 AIME Problem 10]] (Solution 3)<br />
* [[1985_AIME_Problems/Problem_12|1985 AIME Problem 12]] (Solutions 1, 2, 3)<br />
* [[1986_AIME_Problems/Problem_2|1986 AIME Problem 2]] (Solutions 1, 2)<br />
* [[1987_AIME_Problems/Problem_14|1987 AIME Problem 14]] (Solutions 1, 2, 3)<br />
* [[1988_AIME_Problems/Problem_8|1988 AIME Problem 8]] (Solution 1)<br />
* [[1988_AIME_Problems/Problem_13|1988 AIME Problem 13]] (Solution 6)<br />
* [[1989_AIME_Problems/Problem_1|1989 AIME Problem 1]] (Solutions 4, 5)<br />
* [[1989_AIME_Problems/Problem_8|1989 AIME Problem 8]] (Solutions 1, 2, 3)<br />
* [[1989_AIME_Problems/Problem_9|1989 AIME Problem 9]] (Solutions 1, 2, 4)<br />
* [[1990_AIME_Problems/Problem_8|1990 AIME Problem 8]] (Solution, Remark)<br />
* [[1992_AIME_Problems/Problem_6|1992 AIME Problem 6]] (Solution 1)<br />
* [[1993_AIME_Problems/Problem_7|1993 AIME Problem 7]] (Solution 4)<br />
* [[1993_AIME_Problems/Problem_8|1993 AIME Problem 8]] (Solutions 3, 4)<br />
* [[2019_AIME_II_Problems/Problem_7|2019 AIME II Problem 7]] (Diagram)<br />
* [[2020_AIME_I_Problems/Problem_5|2020 AIME I Problem 5]] (Solution 9)<br />
* [[2021_AIME_I_Problems/Problem_1|2021 AIME I Problem 1]] (Solution 1)<br />
* [[2021_AIME_I_Problems/Problem_2|2021 AIME I Problem 2]] (Solution 5)<br />
* [[2021_AIME_I_Problems/Problem_3|2021 AIME I Problem 3]] (Solution 3)<br />
* [[2021_AIME_I_Problems/Problem_7|2021 AIME I Problem 7]] (Remark)<br />
* [[2021_AIME_I_Problems/Problem_8|2021 AIME I Problem 8]] (Solution 1, Remark)<br />
* [[2021_AIME_I_Problems/Problem_9|2021 AIME I Problem 9]] (Diagram, Solution 6)<br />
* [[2021_AIME_I_Problems/Problem_10|2021 AIME I Problem 10]] (Solution 2)<br />
* [[2021_AIME_I_Problems/Problem_11|2021 AIME I Problem 11]] (Solution 1)<br />
* [[2021_AIME_I_Problems/Problem_12|2021 AIME I Problem 12]] (Solution)<br />
* [[2021_AIME_I_Problems/Problem_14|2021 AIME I Problem 14]] (Solutions 2, 3)<br />
* [[2021_AIME_I_Problems/Problem_15|2021 AIME I Problem 15]] (Diagram, Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_1|2021 AIME II Problem 1]] (Solution 3, Remark)<br />
* [[2021_AIME_II_Problems/Problem_2|2021 AIME II Problem 2]] (Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_3|2021 AIME II Problem 3]] (Solution 2)<br />
* [[2021_AIME_II_Problems/Problem_4|2021 AIME II Problem 4]] (Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_5|2021 AIME II Problem 5]] (Solutions 2, 5)<br />
* [[2021_AIME_II_Problems/Problem_6|2021 AIME II Problem 6]] (Solution 3)<br />
* [[2021_AIME_II_Problems/Problem_7|2021 AIME II Problem 7]] (Solution 4)<br />
* [[2021_AIME_II_Problems/Problem_8|2021 AIME II Problem 8]] (Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_9|2021 AIME II Problem 9]] (Solution 1, Remarks)<br />
* [[2021_AIME_II_Problems/Problem_10|2021 AIME II Problem 10]] (Diagram, Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_11|2021 AIME II Problem 11]] (Solution 2)<br />
* [[2021_AIME_II_Problems/Problem_12|2021 AIME II Problem 12]] (Solution 2)<br />
* [[2021_AIME_II_Problems/Problem_13|2021 AIME II Problem 13]] (Solutions 1, 3)<br />
* [[2021_AIME_II_Problems/Problem_14|2021 AIME II Problem 14]] (Diagram, Solution 1)<br />
* [[2021_AIME_II_Problems/Problem_15|2021 AIME II Problem 15]] (Solution 2)<br />
<br />
==External Links==<br />
* [[User_talk:MRENTHUSIASM|User Talk Page]] <br> Welcome to my user talk page here. Feel free to leave any message you like.<br />
* [[User:Flamekhoemberish|Flame Kho's User Page]] <br> Recently I am helping my friend Flame Kho to create his user page. Enjoy his AMC Solutions and artworks! <math>\smiley{}</math></div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Flamekhoemberish&diff=162809User:Flamekhoemberish2021-09-27T20:43:54Z<p>Beautifulmath: /* User Count */</p>
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<div>==User Count==<br />
If this is your first time visiting this page, edit it by incrementing the user count below by one.</font></div><br />
<center><font size="100px">8</font></center><br />
<br />
==Introduction==<br />
Hi Everyone,<br />
<br />
I am Flame Kho. I am currently working in England and quite fluent in both English and Mandarin.<br />
<br />
I have a broad range of interests: mathematics, Cover Chess, classic Chinese songs, travels, etc. I also enjoy creating certificates for chess winners. Visit this page for my interests and artworks. :)<br />
<br />
Below is my upcoming avatar, which I will change two weeks from now.<br />
<br />
[[File:FlameKhoAvatar.jpeg|center|300px]]<br />
~FlameKhoEmberish<br />
<br />
==Mathematics==<br />
I am an amateur problem-solver. I am so proud of my contribution to [[2021_AMC_10A_Problems/Problem_25|2021 AMC 10A Problem 25]] (Solution 3).<br />
<br />
==Cover Chess==<br />
Cover Chess is a variant of Xiangqi (Chinese Chess), where all pieces are covered initially. The game has a considerable amount of luck--even amateur players have a chance of beating masters.<br />
<br />
I managed many Cover Chess tournaments and participated in certificate-making. See my artworks below.<br />
<br />
==Guess Songs==<br />
I am a fan of Chinese classic music. I recognize a lot of songs. If you want to challenge me on guessing songs, I will always be here! :)<br />
<br />
==Artworks==<br />
In this section, I will show you my artworks across different areas. I am the original author for all of the artworks below.<br />
<br />
Hope you enjoy them! :)<br />
<br />
===Certificates===<br />
====Cover Chess====<br />
<center>[[File:Cover Chess Certificate 1.jpeg|450px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Cover Chess Certificate 2.jpeg|450px]]</center><p><br />
<center>[[File:Cover Chess Certificate 3.jpeg|450px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Cover Chess Certificate 7.jpeg|450px]]</center><p><br />
<center>[[File:Cover Chess Certificate 8.jpeg|center|450px]]</center><p><br />
<center>[[File:Cover Chess Certificate 4.jpeg|300px]]&nbsp;&nbsp;&nbsp;&nbsp;[[File:Cover Chess Certificate 5.jpeg|300px]]&nbsp;&nbsp;&nbsp;&nbsp;[[File:Cover Chess Certificate 6.jpeg|300px]]</center><br />
<br />
====Guess Songs====<br />
[[File:GuessSongs.jpeg|center|300px]]<br />
<br />
===Posters===<br />
====Valentine Speed Chess Tournament====<br />
<center>[[File:Season 2.jpeg|300px]][[File:Season 3.jpeg|300px]][[File:Season 4.jpeg|300px]]</center><br />
<center>[[File:Season 5.jpeg|300px]][[File:Season 6.jpeg|300px]][[File:Season 7.jpeg|300px]]</center><br />
<center>[[File:Season 8.jpeg|300px]][[File:Season 9.jpeg|300px]][[File:Season 10.jpeg|300px]]</center><br />
<br />
====Master Challenges====<br />
[[File:Master 1.jpeg|center|600px]]<p><br />
[[File:Master 2.png|center|600px]]<p><br />
[[File:Master 3.jpeg|center|600px]]<br />
<br />
====Other Chess Tournaments====<br />
<center>[[File:Chess Poster 1.jpeg|400px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Chess Poster 2.jpeg|400px]]</center><p><br />
<center>[[File:Chess Poster 3.jpeg|400px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Chess Poster 4.jpeg|400px]]</center><br />
<br />
===Photographs===<br />
[[File:Church.jpeg|center]]<p><br />
[[File:Outdoors.jpeg|center]]<br />
<br />
===Drawings===<br />
[[File:Drawing.jpeg|center|300px]]<br />
<br />
==Cartoons==<br />
[[File:Cartoon.jpeg|center]]<br />
<br />
==Stickers==<br />
Finally, I am a huge fan of stickers. Below are my favorite ones. As you can tell, I love cats in particular.<br />
<center>[[File:Coming.png|250px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Hahahahaha.png|250px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Bad Words.jpg|250px]]</center><p><br />
<center>[[File:Yes.gif|250px]]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[[File:Fighting.gif|250px]]</center><br />
<br />
==Acknowledgements==<br />
I especially thank [[User:MRENTHUSIASM|MRENTHUSIASM]] for creating and editing my user page.</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=2005_AMC_12A_Problems/Problem_12&diff=1585822005 AMC 12A Problems/Problem 122021-07-16T00:18:50Z<p>Beautifulmath: /* Solution 2 */</p>
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<div>== Problem ==<br />
A [[line]] passes through <math>A\ (1,1)</math> and <math>B\ (100,1000)</math>. How many other points with integer coordinates are on the line and strictly between <math>A</math> and <math>B</math>?<br />
<br />
<math><br />
(\mathrm {A}) \ 0 \qquad (\mathrm {B}) \ 2 \qquad (\mathrm {C})\ 3 \qquad (\mathrm {D}) \ 8 \qquad (\mathrm {E})\ 9<br />
</math><br />
<br />
== Solution ==<br />
For convenience’s sake, we can transform <math>A</math> to the origin and <math>B</math> to <math>(99,999)</math> (this does not change the problem). The line <math>AB</math> has the [[equation]] <math>y = \frac{999}{99}x = \frac{111}{11}x</math>. The coordinates are integers if <math>11|x</math>, so the values of <math>x</math> are <math>11, 22 \ldots 88</math>, with a total of <math>8\implies \boxed{\mathrm{(D)}}</math> coordinates.<br />
<br />
== Solution 2 ==<br />
The slope of the line is<math><br />
\frac{1000-1}{100-1}=\frac{111}{11},<br />
</math>so all points on the line have the form <math>(1+11t, 1+111t)</math> for some value of <math>t</math> (the rise is 111 and the run is 11). Such a point has integer coordinates if and only if <math>t</math> is an integer, and the point is strictly between <math>A</math> and <math>B</math> if and only if <math>0<t<9</math>. Thus, there are <math>\boxed{8}</math> points with the required property.<br />
-Paixiao<br />
<br />
== See also ==<br />
{{AMC12 box|year=2005|num-b=11|num-a=13|ab=A}}<br />
<br />
[[Category:Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User_talk:Beautifulmath&diff=153908User talk:Beautifulmath2021-05-19T02:01:20Z<p>Beautifulmath: </p>
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<div>On daily 5:00-6:00 PST</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Beautifulmath&diff=153907User:Beautifulmath2021-05-19T02:00:43Z<p>Beautifulmath: </p>
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<div>https://artofproblemsolving.com/wiki/index.php/User_talk:Beautifulmath</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Beautifulmath&diff=153906User:Beautifulmath2021-05-19T02:00:09Z<p>Beautifulmath: </p>
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<div>artofproblemsolving.com/wiki/index.php?user_talk:BeautifulMath</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Beautifulmath&diff=153905User:Beautifulmath2021-05-19T01:59:57Z<p>Beautifulmath: </p>
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<div>artofproblemsolving.com/wiki/index.php?title=user_talk:BeautifulMath</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User_talk:Beautifulmath&diff=153904User talk:Beautifulmath2021-05-19T01:57:42Z<p>Beautifulmath: Created page with "Hello."</p>
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<div>Hello.</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Beautifulmath&diff=153903User:Beautifulmath2021-05-19T01:57:12Z<p>Beautifulmath: Created page with "Hello."</p>
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<div>Hello.</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User_talk:BeautifulMath&diff=153902User talk:BeautifulMath2021-05-19T01:55:56Z<p>Beautifulmath: Created page with "User:BeautifulMath"</p>
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<div>User:BeautifulMath</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:BeautifulMath&diff=153901User:BeautifulMath2021-05-19T01:55:09Z<p>Beautifulmath: Created page with "Have a betta fish, likes to grow mushrooms (oyster), and read sci-fi. Thanks for reading this page..."</p>
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<div>Have a betta fish, likes to grow mushrooms (oyster), and read sci-fi. <br />
Thanks for reading this page...</div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Piphi&diff=137723User:Piphi2020-11-19T00:38:46Z<p>Beautifulmath: /* User Count */</p>
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<div>{{User:Piphi/Template:Header}}<br />
<br><br />
__NOTOC__<div style="border:2px solid black; -webkit-border-radius: 10px; background:#F0F2F3"><br />
==<font color="black" style="font-family: ITC Avant Garde Gothic Std, Verdana"><div style="margin-left:10px">User Count</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black">If this is your first time visiting this page, edit it by incrementing the user count below by one.</font></div><br />
<center><font size="100px">039</font></center><br />
</div><br />
<div style="border:2px solid black; background:#B1B2B3;-webkit-border-radius: 10px; align:center"><br />
<br />
==<font color="black" style="font-family: ITC Avant Garde Gothic Std, Verdana"><div style="margin-left:10px">About Me</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black">Piphi is the creator of the [[User:Piphi/Games|AoPS Wiki Games by Piphi]], the future of games on AoPS.<br><br />
<br />
Piphi started the signature trend at around May 2020.<br><br />
<br />
Piphi has been very close to winning multiple [[Greed Control]] games, piphi placed 5th in game #18 and 2nd in game #19. Thanks to piphi, Greed Control games have started to be kept track of. Piphi made a spreadsheet that has all of Greed Control history [https://artofproblemsolving.com/community/c19451h2126208p15569802 here].<br><br />
<br />
Piphi also found out who won [[Reaper]] games #1 and #2 as seen [https://artofproblemsolving.com/community/c19451h1826745p15526330 here].<br><br />
<br />
Piphi created the [[AoPS Administrators]] page, added most of the AoPS Admins to it, and created the scrollable table.<br><br />
<br />
Piphi has also added a lot of the info that is in the [[Reaper Archives]].<br><br />
<br />
Piphi has a side-project that is making the Wiki's [[Main Page]] look better, you can check that out [[User:Piphi/AoPS Wiki|here]].<br><br />
<br />
Piphi published Greed Control Game 19 statistics [https://artofproblemsolving.com/community/c19451h2126212 here].<br />
<br />
Piphi has a post that was made an announcement in a official AoPS Forum [https://artofproblemsolving.com/community/c68h2175116 here].<br />
<br />
Piphi is a proud member of [https://artofproblemsolving.com/community/c562043 The Interuniversal GMAAS Society].<br />
<br />
Piphi has won 2 gold trophies at the [https://artofproblemsolving.com/community/c1124279 Asymptote Competition] and is now part of the staff.<br />
</font></div><br />
</div><br />
<div style="border:2px solid black; background:#727373;-webkit-border-radius: 10px; align:center"><br />
<br />
==<font color="#f0f2f3" style="font-family: ITC Avant Garde Gothic Std, Verdana"><div style="margin-left:10px">Goals</div></font>==<br />
<div style="margin-left: 10px; margin-right: 10px; margin-bottom:10px"><font color="#f0f2f3"><br />
You can check out more goals/statistics [[User:Piphi/Statistics|here]].<br />
<br />
A User Count of 500<br />
{{User:Piphi/Template:Progress_Bar|7.4|width=100%}}<br />
<br />
200 subpages of [[User:Piphi]]<br />
{{User:Piphi/Template:Progress_Bar|63.5|width=100%}}<br />
<br />
200 signups for [[User:Piphi/Games|AoPS Wiki Games by Piphi]]<br />
{{User:Piphi/Template:Progress_Bar|47.5|width=100%}}<br />
<br />
Make 10,000 edits<br />
{{User:Piphi/Template:Progress_Bar|20.09|width=100%}}</font></div><br />
</div></div>Beautifulmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Niqhtwolf&diff=137722User:Niqhtwolf2020-11-19T00:38:13Z<p>Beautifulmath: /* User Count */</p>
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<div>==<font color="black" style="font-family: ITC Avant Garde Gothic Std, Verdana"><div style="margin-left:10px">User Count</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black">If this is your first time visiting this page, edit it by incrementing the user count below by one.</font></div><br />
<center><font size="101px">3<br />
</font></center><br />
</div><br />
<div style="border:2px solid black; background:#cccccc;-webkit-border-radius: 10px; align:center"><br />
<br />
==<font color="black" style="font-family: ITC Avant Garde Gothic Std, Verdana"><div style="margin-left:10px">Full list of interests in no specific order</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black"><br />
<br />
Kpop <br><br />
Basketball <br><br />
Tennis <br><br />
Math <br><br />
Reading <br><br />
Writing <br><br />
Minecraft <br><br />
Animal Jam <br><br />
Splatoon 1&2 <br><br />
AoPS <br><br />
Biking <br><br />
Violin <br><br />
Crafts <br><br />
Programming<br><br />
<br />
</font></div><br />
</div><br />
<div style="border:2px solid black; background:#bbbbbb;-webkit-border-radius: 10px; align:center"></div>Beautifulmath