https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Danprathab&feedformat=atomAoPS Wiki - User contributions [en]2024-03-28T15:05:17ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=User:MRENTHUSIASM&diff=168915User:MRENTHUSIASM2021-12-30T16:28:40Z<p>Danprathab: /* 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">87</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:Santa 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 2)<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 1)<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]] (Solutions 1, 3)<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 />
* [[2018_AMC_10B_Problems/Problem_21|2018 AMC 10B Problem 21]] (Solutions 1, 2)<br />
* [[2018_AMC_10B_Problems/Problem_24|2018 AMC 10B Problem 24]] (Diagram, Solution 6)<br />
* [[2020_AMC_10A_Problems/Problem_3|2020 AMC 10A Problem 3]] (Solutions 1, 2)<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]] (Solutions 1, 2)<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, 4, Video Solution)<br />
* [[2021_AMC_10A_Problems/Problem_25|2021 AMC 10A Problem 25]] (Solutions 2, 3, Video Solution)<br />
* [[2021_AMC_10B_Problems/Problem_6|2021 AMC 10B Problem 6]] (Solution 2)<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_17|2021 AMC 10B Problem 17]] (Solution)<br />
* [[2021_AMC_10B_Problems/Problem_23|2021 AMC 10B Problem 23]] (Diagram)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_1|2021 Fall AMC 10A Problem 1]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_2|2021 Fall AMC 10A Problem 2]] (Solution)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_3|2021 Fall AMC 10A Problem 3]] (Solutions 1, 2, 3)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_4|2021 Fall AMC 10A Problem 4]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_6|2021 Fall AMC 10A Problem 6]] (Solution)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_7|2021 Fall AMC 10A Problem 7]] (Solution)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_10|2021 Fall AMC 10A Problem 10]] (Solution)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_11|2021 Fall AMC 10A Problem 11]] (Solution 3)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_12|2021 Fall AMC 10A Problem 12]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_15|2021 Fall AMC 10A Problem 15]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_16|2021 Fall AMC 10A Problem 16]] (Solutions 1, 2)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_17|2021 Fall AMC 10A Problem 17]] (Diagrams, Solution 5)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_18|2021 Fall AMC 10A Problem 18]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_19|2021 Fall AMC 10A Problem 19]] (Diagram)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_20|2021 Fall AMC 10A Problem 20]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_21|2021 Fall AMC 10A Problem 21]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_22|2021 Fall AMC 10A Problem 22]] (Diagram)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_24|2021 Fall AMC 10A Problem 24]] (Solution 1)<br />
* [[2021_Fall_AMC_10A_Problems/Problem_25|2021 Fall AMC 10A Problem 25]] (Solution 2)<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]] (Solutions 1, 3)<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, 3)<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_15|2018 AMC 12B Problem 15]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_16|2018 AMC 12B Problem 16]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_17|2018 AMC 12B Problem 17]] (Solutions 1, 2)<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 />
* [[2018_AMC_12B_Problems/Problem_19|2018 AMC 12B Problem 19]]: same as [[2018_AMC_10B_Problems/Problem_21|2018 AMC 10B Problem 21]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_20|2018 AMC 12B Problem 20]]: same as [[2018_AMC_10B_Problems/Problem_24|2018 AMC 10B Problem 24]] (Diagram, Solution 6)<br />
* [[2018_AMC_12B_Problems/Problem_21|2018 AMC 12B Problem 21]] (Diagram, Solution)<br />
* [[2018_AMC_12B_Problems/Problem_22|2018 AMC 12B Problem 22]] (Solutions 1, 2)<br />
* [[2018_AMC_12B_Problems/Problem_23|2018 AMC 12B Problem 23]] (Diagram, Solutions 1, 2, 3)<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 2)<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_8|2021 AMC 12A Problem 8]] (Solution)<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, Video Solution)<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 2)<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 1)<br />
* [[2021_AMC_12B_Problems/Problem_20|2021 AMC 12B Problem 20]] (Solution 1)<br />
* [[2021_AMC_12B_Problems/Problem_21|2021 AMC 12B Problem 21]] (Solution 2)<br />
* [[2021_AMC_12B_Problems/Problem_23|2021 AMC 12B Problem 23]] (Solution 4)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_1|2021 Fall AMC 12A Problem 1]]: same as [[2021_Fall_AMC_10A_Problems/Problem_1|2021 Fall AMC 10A Problem 1]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_2|2021 Fall AMC 12A Problem 2]]: same as [[2021_Fall_AMC_10A_Problems/Problem_2|2021 Fall AMC 10A Problem 2]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_3|2021 Fall AMC 12A Problem 3]]: same as [[2021_Fall_AMC_10A_Problems/Problem_4|2021 Fall AMC 10A Problem 4]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_5|2021 Fall AMC 12A Problem 5]]: same as [[2021_Fall_AMC_10A_Problems/Problem_6|2021 Fall AMC 10A Problem 6]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_6|2021 Fall AMC 12A Problem 6]]: same as [[2021_Fall_AMC_10A_Problems/Problem_7|2021 Fall AMC 10A Problem 7]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_7|2021 Fall AMC 12A Problem 7]]: same as [[2021_Fall_AMC_10A_Problems/Problem_10|2021 Fall AMC 10A Problem 10]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_9|2021 Fall AMC 12A Problem 9]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_10|2021 Fall AMC 12A Problem 10]]: same as [[2021_Fall_AMC_10A_Problems/Problem_12|2021 Fall AMC 10A Problem 12]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_12|2021 Fall AMC 12A Problem 12]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_13|2021 Fall AMC 12A Problem 13]] (Diagram, Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_16|2021 Fall AMC 12A Problem 16]] (Solution)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_17|2021 Fall AMC 12A Problem 17]]: same as [[2021_Fall_AMC_10A_Problems/Problem_20|2021 Fall AMC 10A Problem 20]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_18|2021 Fall AMC 12A Problem 18]]: same as [[2021_Fall_AMC_10A_Problems/Problem_21|2021 Fall AMC 10A Problem 21]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_23|2021 Fall AMC 12A Problem 23]]: same as [[2021_Fall_AMC_10A_Problems/Problem_25|2021 Fall AMC 10A Problem 25]] (Solution 2)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_24|2021 Fall AMC 12A Problem 24]] (Solution 1)<br />
* [[2021_Fall_AMC_12A_Problems/Problem_25|2021 Fall AMC 12A Problem 25]] (Solution 1)<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 3, 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 1)<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]] (Diagram, 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, 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 />
==AoPS Forums==<br />
* [https://artofproblemsolving.com/community/c2686156_hedgehog_military HEDGEHOG MILITARY] <br> Let's have a good time in this forum. Feel free to discuss math classes, math competitions, AoPS Wiki contributions, funny pictures, emojis, and ... HEDGEHOGS! :)<br />
<br />
==Artworks==<br />
In this section, I will show you my artworks of certificates and posters. Hope you enjoy them! :)<br />
<br />
I especially thank [[User:Flamekhoemberish|Flame Kho]] for teaching me how to use the Chuangkit design platform.<br />
<br />
===Hall of Fame in MATHCOUNTS/AMC 8 Basics (2557)===<br />
[[File:2021 AMC 8 Perfect Scorers.png|center|750px]] <p><br />
<br />
[[File:2557 Gold.png|center|750px]] <p><br />
<br />
[[File:2557 Silver.png|center|750px]] <p><br />
<br />
[[File:2557 Bronze.png|center|750px]]<br />
<br />
===Hall of Fame in MATHCOUNTS/AMC 8 Basics (2786)===<br />
[[File:2846 2022 AMC 8 Perfect Scorers.png|center|500px]] <p><br />
<br />
[[File:2846 Gold.png|center|750px]] <p><br />
<br />
[[File:2846 Silver.png|center|750px]] <p><br />
<br />
[[File:2846 Bronze 1.png|center|750px]] <p><br />
<br />
[[File:2846 Bronze 2.png|center|750px]]<br />
<br />
===Most Prominent Member of Boston Xiangqi Community===<br />
[[File:Funny Guy.png|center|750px]]<br />
<br />
==Cats==<br />
As you might know, I am particularly fond of cats. My family has raised more than ten cats. These little angels are so adorable! MEOW MEOW MEOW!!! 🐱🐱🐱<br />
<br />
===Luna===<br />
[[File:Luna.jpg|center|300px]]<br />
<br />
===Kidney Bean===<br />
<center>[[File:Kidney Bean 1.jpg|300px]]&nbsp;&nbsp;&nbsp;[[File:Kidney Bean 2.jpg|300px]]</center><br />
<br />
===Jin Bao===<br />
[[File:Jin Bao.jpg|center|300px]]<br />
<br />
===Gray Gray===<br />
[[File:Little Gray Gray 1.jpg|center|300px]] <p><br />
<br />
<center>[[File:Little Gray Gray 2.jpg|450px]]&nbsp;&nbsp;&nbsp;[[File:Little Gray Gray 3.jpg|450px]]</center><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>Danprathabhttps://artofproblemsolving.com/wiki/index.php?title=2021_Fall_AMC_10B_Problems/Problem_2&diff=1662472021 Fall AMC 10B Problems/Problem 22021-11-24T23:39:03Z<p>Danprathab: </p>
<hr />
<div>==Problem==<br />
<br />
What is the area of the shaded figure shown below?<br />
<asy><br />
size(200);<br />
defaultpen(linewidth(0.4)+fontsize(12));<br />
pen s = linewidth(0.8)+fontsize(8);<br />
<br />
pair O,X,Y;<br />
O = origin;<br />
X = (6,0);<br />
Y = (0,5);<br />
fill((1,0)--(3,5)--(5,0)--(3,2)--cycle, palegray+opacity(0.2));<br />
for (int i=1; i<7; ++i)<br />
{<br />
draw((i,0)--(i,5), gray+dashed);<br />
label("${"+string(i)+"}$", (i,0), 2*S);<br />
if (i<6)<br />
{<br />
draw((0,i)--(6,i), gray+dashed);<br />
label("${"+string(i)+"}$", (0,i), 2*W);<br />
}<br />
}<br />
label("$0$", O, 2*SW);<br />
draw(O--X+(0.15,0), EndArrow);<br />
draw(O--Y+(0,0.15), EndArrow);<br />
draw((1,0)--(3,5)--(5,0)--(3,2)--(1,0), black+1.5);<br />
</asy><br />
<br />
<math>(\textbf{A})\: 4\qquad(\textbf{B}) \: 6\qquad(\textbf{C}) \: 8\qquad(\textbf{D}) \: 10\qquad(\textbf{E}) \: 12</math><br />
<br />
==Solution #1==<br />
<br />
We have <math>2</math> isosceles triangles. Thus, the area of the shaded region is <math>\frac{1}{2} \cdot 5 \cdot 4 - \left(\frac{1}{2} \cdot 4 \cdot 2\right) = 10 - 4 = 6.</math> Thus our answer is <math>\boxed{(\textbf{B}.)}.</math> <br />
<br />
~NH14<br />
<br />
<br />
==Solution #2==<br />
<br />
As we can see, the shape is symmetrical, so it will be equally valid to simply calculate one of the half's area and multiply by 2. One half's area is <math>\frac{bh}2</math>, so two halves would be <math>bh=3\cdot2=6</math>. Thus our answer is <math>\boxed{(\textbf{B}.)}.</math><br />
<br />
~Hefei417, or 陆畅 Sunny from China<br />
<br />
<br />
==Solution #3 (Overkill)==<br />
We start by finding the points. The outlined shape is made up of <math>(1,0),(3,5),(5,0),(3,2)</math>. By the Shoelace Theorem, we find the area to be <math>6</math>, or <math>\boxed{B}</math>.<br />
<br />
~Taco12<br />
<br />
<br />
==Solution #4 (Pick's Theorem)==<br />
<br />
We can use Pick's Theorem. We have <math>4</math> interior points and <math>6</math> boundary points. By Pick's Theorem, we get <math>4+\frac{6}{2}-1 = 4+3-1 = 6.</math> Checking our answer choices, we find our answer to be <math>\boxed{B}</math>.<br />
<br />
~danprathab<br />
<br />
==Video Solution by Interstigation==<br />
https://youtu.be/p9_RH4s-kBA?t=110<br />
<br />
==See Also==<br />
{{AMC10 box|year=2021 Fall|ab=B|num-a=3|num-b=1}}<br />
{{MAA Notice}}</div>Danprathabhttps://artofproblemsolving.com/wiki/index.php?title=User:OlympusHero&diff=159701User:OlympusHero2021-08-07T02:29:11Z<p>Danprathab: /* User Count */</p>
<hr />
<div>OlympusHero's Page:<br />
<br><br />
__NOTOC__<div style="border:2px solid black; -webkit-border-radius: 10px; background:#dddddd"><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="107px"> 320 users have visted this!<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">About Me</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black">OlympusHero is currently borderline AIME.<br><br />
<br />
OlympusHero is 11 years old.<br><br />
<br />
OlympusHero scored 40/46 when mocking the 2019 MATHCOUNTS State test, and got silver on the 2020 online MATHCOUNTS State.<br><br />
<br />
OlympusHero is a pro at math and chess.<br />
<br />
OlympusHero for brown MOP 2021.<br />
<br />
OlympusHero was #1 at the 2017 Chess World Cadets U8 (He was 7 years old)<br />
<br />
OlympusHero is pro at joking believe it.<br />
<br />
OlympusHero is much better than Rusczyk at math yes or no, no one knows. (he's not)<br />
<br />
-----------<br />
<br />
OlympusHero is very pro and is much better than bestzack66 in MC trainer, Alcumus, and FTW. ~bestzack66<br />
<br />
OlympusHero will always beat hh99754539 in everything, whether it is MATHCOUNTS trainer, Alcumus, or FTW. ~hh99754539<br />
</font></div><br />
</div><br />
<div style="border:2px solid black; background:#bbbbbb;-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">Goals</div></font>==<br />
<div style="margin-left: 10px; margin-right: 10px; margin-bottom:10px">A User Count of 300<br />
<br />
Make AIME 2021 (Currently borderline)<br />
<br />
Get 5 or more on AIME I 2021 (Mocked a 3 on the 2020 AIME I a few months ago)<br />
<br />
- some months later; guess I have improved (got from 3-->6 for 2020 AIME I) sadly sillies killed me crap<br />
<br />
Get to 40 or more on the MATHCOUNTS Trainer Nationals Level (25/40)<br />
<br />
Get a perfect score and First Place in IMO 2021.<br />
</div><br />
</div></div>Danprathabhttps://artofproblemsolving.com/wiki/index.php?title=User:OlympusHero&diff=153339User:OlympusHero2021-05-07T18:29:10Z<p>Danprathab: /* User Count */</p>
<hr />
<div>OlympusHero's Page:<br />
<br><br />
__NOTOC__<div style="border:2px solid black; -webkit-border-radius: 10px; background:#dddddd"><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="107px"> 81 users have visted this!<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">About Me</div></font>==<br />
<div style="margin-left: 10px; margin-bottom:10px"><font color="black">OlympusHero is currently borderline AIME.<br><br />
<br />
OlympusHero is 10 years old.<br><br />
<br />
OlympusHero scored 47/46 (got an extra point for finishing the test under 10 minutes) when mocking the 2019 MATHCOUNTS State test, and got silver on the 2020 online MATHCOUNTS State.<br><br />
<br />
OlympusHero is a pro at math and chess<br />
<br />
OlympusHero for brown MOP 2021<br />
<br />
OlympusHero was #1 at the 2017 Chess World Cadets U8 (He was 7 years old)<br />
<br />
OlympusHero is pro at joking believe it.<br />
<br />
OlympusHero is much better than Rusczyk at math yes or no, no one knows. (he's not)<br />
<br />
-----------<br />
<br />
OlympusHero is very pro and is much better than bestzack66 in MC trainer, Alcumus, and FTW. ~bestzack66<br />
</font></div><br />
</div><br />
<div style="border:2px solid black; background:#bbbbbb;-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">Goals</div></font>==<br />
<div style="margin-left: 10px; margin-right: 10px; margin-bottom:10px">A User Count of 300<br />
<br />
Make AIME 2021 (Currently borderline)<br />
<br />
Get 5 or more on AIME I 2021 (Mocked a 3 on the 2020 AIME I a few months ago)<br />
<br />
- some months later; guess I have improved (got from 3-->6 for 2020 AIME I) sadly sillies killed me crap<br />
<br />
Get to 40 or more on the MATHCOUNTS Trainer Nationals Level (25/40)<br />
<br />
Get a perfect score and First Place in IMO 2021.<br />
</div><br />
</div></div>Danprathab