# User:MRENTHUSIASM

## Contents

## User Count

If this is your first time visiting this page, then edit it by incrementing the user count below by one.

## Introduction

Hi Everyone,

I am a hedgehog who likes Message Board halping, funny pictures, emoji wars, and AoPS Wiki contributions. Keep these fun things coming!

This hedgehog represents my attitude towards mathematics--victorious and enthusiastic!

And here is my personified self-portrait:

~MRENTHUSIASM

## AoPS Bio

Jerry graduated from Northeastern University in 2018 as a mathematics and computer science combined major. He has eleven years of experience working with students. He has served as an AoPS instructor and a message board moderator since 2019. 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. In his mind, nothing is more rewarding than educating tomorrow’s bright minds. In 2020 he published the book English-Chinese Mathematics Encyclopedia: Algebra, Geometry, and Pre-Calculus in Tsinghua University Press in China. 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.

## AoPS Wiki Contributions

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. **In any of my solutions, if you find flaws and/or want major revisions, then please contact me via my user talk page or the private messaging system before you take action. I am sure that we can work things out.**

Thank you for your cooperation, and hope you enjoy reading my solutions.

Finally, here is my YouTube channel (MRENTHUSIASM) for the video solutions. Go ahead and subscribe--you know you want to.

~MRENTHUSIASM

### AJHSME / AMC 8

- 2007 AMC 8 Problem 8 (Solutions 1, 2)
- 2007 AMC 8 Problem 10 (Solution)
- 2009 AMC 8 Problem 4 (Solution)
- 2017 AMC 8 Problem 24 (Solution 2)
- 2020 AMC 8 Problem 1 (Solutions 2, 3)
- 2020 AMC 8 Problem 3 (Solution 1)
- 2020 AMC 8 Problem 4 (Solutions 2, 4)
- 2022 AMC 8 Problem 3 (Solution)
- 2022 AMC 8 Problem 4 (Solution)
- 2022 AMC 8 Problem 5 (Solution)
- 2022 AMC 8 Problem 6 (Solution)
- 2022 AMC 8 Problem 8 (Solution)
- 2022 AMC 8 Problem 9 (Solution)
- 2022 AMC 8 Problem 10 (Solution)
- 2022 AMC 8 Problem 13 (Solution)
- 2022 AMC 8 Problem 14 (Solution)
- 2022 AMC 8 Problem 16 (Solutions 1, 2)
- 2022 AMC 8 Problem 18 (Solution 1)
- 2022 AMC 8 Problem 20 (Solution 2)
- 2022 AMC 8 Problem 22 (Solution)
- 2022 AMC 8 Problem 24 (Remark)
- 2022 AMC 8 Problem 25 (Solution 1)

### AMC 10

- 2004 AMC 10A Problem 24 (Solutions 1, 2)
- 2007 AMC 10A Problem 20 (Solutions 1, 2, 3, 4, 5, 6, 7)
- 2009 AMC 10B Problem 1 (Solutions 1, 2, 3)
- 2012 AMC 10B Problem 10 (Solutions 1, 2)
- 2018 AMC 10A Problem 1 (Solution)
- 2018 AMC 10A Problem 5 (Solution 1)
- 2018 AMC 10A Problem 7 (Solutions 1, 2)
- 2018 AMC 10A Problem 8 (Solution 3)
- 2018 AMC 10A Problem 17 (Solution 4)
- 2018 AMC 10A Problem 21 (Remark)
- 2018 AMC 10A Problem 23 (Solution 1)
- 2018 AMC 10A Problem 25 (Solutions 1, 3)
- 2018 AMC 10B Problem 2 (Solutions 1, 2)
- 2018 AMC 10B Problem 15 (Solutions 1, 3)
- 2018 AMC 10B Problem 19 (Solution 1)
- 2018 AMC 10B Problem 20 (Solutions 1, 2)
- 2018 AMC 10B Problem 21 (Solutions 1, 2)
- 2018 AMC 10B Problem 24 (Diagram, Solution 6)
- 2020 AMC 10A Problem 3 (Solutions 1, 2)
- 2020 AMC 10A Problem 5 (Solution 3)
- 2020 AMC 10A Problem 11 (Solution 5)
- 2020 AMC 10A Problem 17 (Solution 1)
- 2020 AMC 10A Problem 24 (Solution 8)
- 2020 AMC 10A Problem 25 (Solution 2)
- 2020 AMC 10B Problem 3 (Solution 1)
- 2020 AMC 10B Problem 4 (Solution 3)
- 2020 AMC 10B Problem 8 (Solutions 1, 2)
- 2020 AMC 10B Problem 13 (Solution 1)
- 2020 AMC 10B Problem 15 (Solutions 1, 3)
- 2020 AMC 10B Problem 23 (Solution 1)
- 2021 AMC 10A Problem 1 (Solution 2)
- 2021 AMC 10A Problem 2 (Solutions 1, 2, 3, 4)
- 2021 AMC 10A Problem 3 (Solution 3)
- 2021 AMC 10A Problem 4 (Solutions 1, 3)
- 2021 AMC 10A Problem 5 (Solutions 1, 2, 3)
- 2021 AMC 10A Problem 6 (Solutions 1, 2)
- 2021 AMC 10A Problem 7 (Solutions 1, 3)
- 2021 AMC 10A Problem 8 (Solutions 1, 2, 3)
- 2021 AMC 10A Problem 9 (Solution 2)
- 2021 AMC 10A Problem 10 (Solution 7)
- 2021 AMC 10A Problem 11 (Solutions 1, 3)
- 2021 AMC 10A Problem 12 (Solution 1)
- 2021 AMC 10A Problem 13 (Solutions 1, 2, 3)
- 2021 AMC 10A Problem 17 (Diagram, Solutions 1, 2)
- 2021 AMC 10A Problem 18 (Solutions 1, 4)
- 2021 AMC 10A Problem 20 (Solutions 2, 3)
- 2021 AMC 10A Problem 21 (Diagram, Solution, Video Solution)
- 2021 AMC 10A Problem 22 (Solution 2, Video Solution)
- 2021 AMC 10A Problem 23 (Solution 3, Video Solution)
- 2021 AMC 10A Problem 24 (Diagram, Solutions 1, 2, 4, Video Solution)
- 2021 AMC 10A Problem 25 (Solutions 2, 3, Video Solution)
- 2021 AMC 10B Problem 6 (Solution 2)
- 2021 AMC 10B Problem 7 (Solution)
- 2021 AMC 10B Problem 8 (Solutions 1, 2, 3)
- 2021 AMC 10B Problem 17 (Solution)
- 2021 AMC 10B Problem 23 (Diagram)
- 2021 Fall AMC 10A Problem 1 (Solution 1)
- 2021 Fall AMC 10A Problem 2 (Solution)
- 2021 Fall AMC 10A Problem 3 (Solutions 1, 2, 3)
- 2021 Fall AMC 10A Problem 4 (Solution 1)
- 2021 Fall AMC 10A Problem 6 (Solution)
- 2021 Fall AMC 10A Problem 7 (Solution)
- 2021 Fall AMC 10A Problem 10 (Solution)
- 2021 Fall AMC 10A Problem 11 (Solution 3)
- 2021 Fall AMC 10A Problem 12 (Solution 1)
- 2021 Fall AMC 10A Problem 15 (Solution 1)
- 2021 Fall AMC 10A Problem 16 (Solutions 1, 2)
- 2021 Fall AMC 10A Problem 17 (Diagrams, Solution 5)
- 2021 Fall AMC 10A Problem 18 (Solution 1)
- 2021 Fall AMC 10A Problem 19 (Diagram)
- 2021 Fall AMC 10A Problem 20 (Solution 1)
- 2021 Fall AMC 10A Problem 21 (Solution 1)
- 2021 Fall AMC 10A Problem 22 (Diagram)
- 2021 Fall AMC 10A Problem 24 (Solution 1)
- 2021 Fall AMC 10A Problem 25 (Solution 2)
- 2021 Fall AMC 10B Problem 2 (Solutions 1, 2)
- 2021 Fall AMC 10B Problem 4 (Solutions 1, 2)
- 2021 Fall AMC 10B Problem 7 (Solution 1)

### AHSME / AMC 12

- 1976 AHSME Problem 24 (Solution)
- 1976 AHSME Problem 25 (Solution)
- 1976 AHSME Problem 27 (Solutions 1, 2)
- 1976 AHSME Problem 28 (Solution)
- 1976 AHSME Problem 30 (Solution)
- 1978 AHSME Problem 20 (Solution)
- 1982 AHSME Problem 19 (Solution)
- 1982 AHSME Problem 21 (Solution)
- 1982 AHSME Problem 23 (Solutions 1, 2)
- 1982 AHSME Problem 27 (Solution)
- 1982 AHSME Problem 28 (Solution)
- 1982 AHSME Problem 29 (Solution)
- 1982 AHSME Problem 30 (Solution)
- 1990 AHSME Problem 26 (Solutions 1, 2)
- 1991 AHSME Problem 6 (Solution)
- 1991 AHSME Problem 20 (Solution)
- 1991 AHSME Problem 27 (Solution)
- 2004 AMC 12A Problem 16 (Solution)
- 2004 AMC 12A Problem 17: same as 2004 AMC 10A Problem 24 (Solutions 1, 2)
- 2009 AMC 12B Problem 1: same as 2009 AMC 10B Problem 1 (Solutions 1, 2, 3)
- 2014 AMC 12A Problem 18 (Solution 1)
- 2018 AMC 12A Problem 2 (Solutions 1, 2)
- 2018 AMC 12A Problem 4: same as 2018 AMC 10A Problem 5 (Solution 1)
- 2018 AMC 12A Problem 7: same as 2018 AMC 10A Problem 7 (Solutions 1, 2)
- 2018 AMC 12A Problem 12: same as 2018 AMC 10A Problem 17 (Solution 4)
- 2018 AMC 12A Problem 14 (Solutions 1, 2, 3, 4, 5)
- 2018 AMC 12A Problem 16: same as 2018 AMC 10A Problem 21 (Remark)
- 2018 AMC 12A Problem 17: same as 2018 AMC 10A Problem 23 (Solution 1)
- 2018 AMC 12A Problem 19 (Solution 1)
- 2018 AMC 12A Problem 21 (Solution 1)
- 2018 AMC 12A Problem 22 (Solutions 1, 2, 3)
- 2018 AMC 12A Problem 23 (Diagram, Solution 2)
- 2018 AMC 12A Problem 24 (Solutions 1, 2, 3)
- 2018 AMC 12A Problem 25: same as 2018 AMC 10A Problem 25 (Solutions 1, 3)
- 2018 AMC 12B Problem 2: same as 2018 AMC 10B Problem 2 (Solutions 1, 2)
- 2018 AMC 12B Problem 4 (Solution)
- 2018 AMC 12B Problem 6 (Solutions 1, 2)
- 2018 AMC 12B Problem 8 (Solution)
- 2018 AMC 12B Problem 9 (Solutions 1, 2, 3, 4, 5, 6)
- 2018 AMC 12B Problem 11: same as 2018 AMC 10B Problem 15 (Solutions 1, 3)
- 2018 AMC 12B Problem 12 (Solution)
- 2018 AMC 12B Problem 13 (Solutions 1, 2, 3)
- 2018 AMC 12B Problem 14: same as 2018 AMC 10B Problem 19 (Solution 1)
- 2018 AMC 12B Problem 15 (Solutions 1, 2)
- 2018 AMC 12B Problem 16 (Solutions 1, 2)
- 2018 AMC 12B Problem 17 (Solutions 1, 2)
- 2018 AMC 12B Problem 18: same as 2018 AMC 10B Problem 20 (Solutions 1, 2)
- 2018 AMC 12B Problem 19: same as 2018 AMC 10B Problem 21 (Solutions 1, 2)
- 2018 AMC 12B Problem 20: same as 2018 AMC 10B Problem 24 (Diagram, Solution 6)
- 2018 AMC 12B Problem 21 (Diagram, Solution)
- 2018 AMC 12B Problem 22 (Solutions 1, 2)
- 2018 AMC 12B Problem 23 (Diagram, Solutions 1, 2, 3)
- 2020 AMC 12A Problem 1 (Solution 3)
- 2020 AMC 12A Problem 6 (Solution 2)
- 2020 AMC 12A Problem 8: same as 2020 AMC 10A Problem 11 (Solution 5)
- 2020 AMC 12A Problem 9 (Solution)
- 2020 AMC 12A Problem 10 (Solutions 1, 2, 5)
- 2020 AMC 12A Problem 15 (Solutions 1, 2)
- 2020 AMC 12A Problem 23: same as 2020 AMC 10A Problem 25 (Solution 2)
- 2020 AMC 12A Problem 25 (Solution 1, Remark)
- 2020 AMC 12B Problem 3: same as 2020 AMC 10B Problem 3 (Solution 1)
- 2020 AMC 12B Problem 4: same as 2020 AMC 10B Problem 4 (Solution 3)
- 2020 AMC 12B Problem 5 (Solution 1)
- 2020 AMC 12B Problem 6 (Solution 2)
- 2020 AMC 12B Problem 10 (Diagram, Solution 2)
- 2020 AMC 12B Problem 12 (Diagram)
- 2020 AMC 12B Problem 13 (Solutions 1, 4)
- 2020 AMC 12B Problem 19: same as 2020 AMC 10B Problem 23 (Solution 1)
- 2021 AMC 12A Problem 2 (Solutions 2, 3)
- 2021 AMC 12A Problem 3: same as 2021 AMC 10A Problem 3 (Solution 3)
- 2021 AMC 12A Problem 4: same as 2021 AMC 10A Problem 7 (Solutions 1, 3)
- 2021 AMC 12A Problem 5: same as 2021 AMC 10A Problem 8 (Solutions 1, 2, 3)
- 2021 AMC 12A Problem 6 (Solutions 2, 3)
- 2021 AMC 12A Problem 7: same as 2021 AMC 10A Problem 9 (Solution 2)
- 2021 AMC 12A Problem 8 (Solution)
- 2021 AMC 12A Problem 9: same as 2021 AMC 10A Problem 10 (Solution 7)
- 2021 AMC 12A Problem 10: same as 2021 AMC 10A Problem 12 (Solution 1)
- 2021 AMC 12A Problem 11 (Solutions 1, 2, 3)
- 2021 AMC 12A Problem 13 (Solutions 2, 3)
- 2021 AMC 12A Problem 14 (Solutions 1, 2, 3)
- 2021 AMC 12A Problem 15 (Solutions 1, 2, 4)
- 2021 AMC 12A Problem 17: same as 2021 AMC 10A Problem 17 (Diagram, Solutions 1, 2)
- 2021 AMC 12A Problem 18: same as 2021 AMC 10A Problem 18 (Solutions 1, 4)
- 2021 AMC 12A Problem 19 (Solutions 1, 2, 3)
- 2021 AMC 12A Problem 21 (Solution 2, Video Solution)
- 2021 AMC 12A Problem 22 (Solutions 1, 2, 3, 4, 5)
- 2021 AMC 12A Problem 23: same as 2021 AMC 10A Problem 23 (Solution 3, Video Solution)
- 2021 AMC 12A Problem 24 (Solution 1)
- 2021 AMC 12A Problem 25 (Solution 1)
- 2021 AMC 12B Problem 4: same as 2021 AMC 10B Problem 6 (Solution 2)
- 2021 AMC 12B Problem 11 (Solution 4)
- 2021 AMC 12B Problem 14 (Solution 1)
- 2021 AMC 12B Problem 20 (Solution 1)
- 2021 AMC 12B Problem 21 (Solution 2)
- 2021 AMC 12B Problem 23 (Solution 4)
- 2021 Fall AMC 12A Problem 1: same as 2021 Fall AMC 10A Problem 1 (Solution 1)
- 2021 Fall AMC 12A Problem 2: same as 2021 Fall AMC 10A Problem 2 (Solution)
- 2021 Fall AMC 12A Problem 3: same as 2021 Fall AMC 10A Problem 4 (Solution 1)
- 2021 Fall AMC 12A Problem 5: same as 2021 Fall AMC 10A Problem 6 (Solution)
- 2021 Fall AMC 12A Problem 6: same as 2021 Fall AMC 10A Problem 7 (Solution)
- 2021 Fall AMC 12A Problem 7: same as 2021 Fall AMC 10A Problem 10 (Solution)
- 2021 Fall AMC 12A Problem 9 (Solution)
- 2021 Fall AMC 12A Problem 10: same as 2021 Fall AMC 10A Problem 12 (Solution 1)
- 2021 Fall AMC 12A Problem 12 (Solution)
- 2021 Fall AMC 12A Problem 13 (Diagram, Solution 1)
- 2021 Fall AMC 12A Problem 16 (Solution)
- 2021 Fall AMC 12A Problem 17: same as 2021 Fall AMC 10A Problem 20 (Solution 1)
- 2021 Fall AMC 12A Problem 18: same as 2021 Fall AMC 10A Problem 21 (Solution 1)
- 2021 Fall AMC 12A Problem 23: same as 2021 Fall AMC 10A Problem 25 (Solution 2)
- 2021 Fall AMC 12A Problem 24 (Solution 1)
- 2021 Fall AMC 12A Problem 25 (Solution 1)
- 2021 Fall AMC 12B Problem 2: same as 2021 Fall AMC 10B Problem 2 (Solutions 1, 2)
- 2021 Fall AMC 12B Problem 3: same as 2021 Fall AMC 10B Problem 4 (Solutions 1, 2)
- 2021 Fall AMC 12B Problem 5: same as 2021 Fall AMC 10B Problem 7 (Solution 1)
- 2021 Fall AMC 12B Problem 10 (Solution)
- 2021 Fall AMC 12B Problem 12 (Solutions 1, 3)
- 2021 Fall AMC 12B Problem 17 (Solution 4)
- 2021 Fall AMC 12B Problem 18 (Solution 1)

### AIME

- 1984 AIME Problem 4 (Solutions 1, 2)
- 1984 AIME Problem 10 (Solution 3)
- 1985 AIME Problem 12 (Solutions 1, 2, 3)
- 1986 AIME Problem 2 (Solutions 1, 2)
- 1987 AIME Problem 14 (Solutions 1, 2, 3)
- 1988 AIME Problem 8 (Solution 1)
- 1988 AIME Problem 13 (Solution 6)
- 1989 AIME Problem 1 (Solutions 3, 5)
- 1989 AIME Problem 8 (Solutions 1, 2, 3)
- 1989 AIME Problem 9 (Solutions 1, 2, 4)
- 1990 AIME Problem 8 (Solution, Remark)
- 1992 AIME Problem 6 (Solution 1)
- 1993 AIME Problem 7 (Solution 1)
- 1993 AIME Problem 8 (Solutions 3, 4)
- 2019 AIME II Problem 7 (Diagram)
- 2020 AIME I Problem 5 (Solution 9)
- 2021 AIME I Problem 1 (Solution 1)
- 2021 AIME I Problem 2 (Solution 5)
- 2021 AIME I Problem 3 (Solution 3)
- 2021 AIME I Problem 7 (Remark)
- 2021 AIME I Problem 8 (Solution 1, Remark)
- 2021 AIME I Problem 9 (Diagram, Solution 1)
- 2021 AIME I Problem 10 (Solution 2)
- 2021 AIME I Problem 11 (Diagram, Solution 1)
- 2021 AIME I Problem 12 (Solution)
- 2021 AIME I Problem 14 (Solutions 2, 3)
- 2021 AIME I Problem 15 (Diagram, Solution 1)
- 2021 AIME II Problem 1 (Solution 3, Remark)
- 2021 AIME II Problem 2 (Solution 1)
- 2021 AIME II Problem 3 (Solution 2)
- 2021 AIME II Problem 4 (Solution 1)
- 2021 AIME II Problem 5 (Solutions 2, 5)
- 2021 AIME II Problem 6 (Solution 3)
- 2021 AIME II Problem 7 (Solution 3)
- 2021 AIME II Problem 8 (Solution 1)
- 2021 AIME II Problem 9 (Solution, Remarks)
- 2021 AIME II Problem 10 (Diagram, Solution 1)
- 2021 AIME II Problem 11 (Solution 2)
- 2021 AIME II Problem 12 (Solution 2)
- 2021 AIME II Problem 13 (Solutions 1, 3)
- 2021 AIME II Problem 14 (Diagram, Solution 1)
- 2021 AIME II Problem 15 (Solution 2)
- 2022 AIME I Problem 1 (Solutions 1, 2, Video Solution)
- 2022 AIME I Problem 2 (Solution 1)
- 2022 AIME I Problem 3 (Diagram)
- 2022 AIME I Problem 4 (Solution 1)
- 2022 AIME I Problem 5 (Solution 2)
- 2022 AIME I Problem 7 (Solution)
- 2022 AIME I Problem 8 (Diagram)

## AoPS Forums

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!

## Publications

* English-Chinese Mathematics Encyclopedia: Algebra, Geometry, and Pre-Calculus* (Tsinghua University Press in Beijing, China)

## Artworks

In this section, I will show you my artworks of certificates and posters. Hope you enjoy them!

I especially thank Flame Kho for teaching me how to use the Chuangkit design platform.

### Hall of Fame in MATHCOUNTS/AMC 8 Basics (2557)

### Hall of Fame in MATHCOUNTS/AMC 8 Basics (2786)

### Hall of Fame in MATHCOUNTS/AMC 8 Basics (3011)

We will see about that--designing templates now ...

### Most Prominent Member of Boston Xiangqi Community

## Cats

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!!! 🐱🐱🐱

### Luna

### Kidney Bean

### Jin Bao

### Gray Gray

## External Links

- User Talk Page

Welcome to my user talk page here. Feel free to leave any message you like. - Flame Kho's User Page

Recently I am helping my friend Flame Kho to create his user page. Enjoy his AMC Solutions and artworks!