2014 IMO:
A Brief Reflection
Evan Chen
August 1, 2014
This report describes my experiences as a contestant for the Taiwanese IMO 2014
team. I draw several comparisons between the Taiwanese selection c
Olympiad Inequalities
Evan Chen
April 30, 2014
The goal of this document is to provide a easier introduction to olympiad
inequalities than the standard exposition Olympiad Inequalities, by Thomas
Mild
Team Selection Test Selection Test Solutions
1. Let 9 denote the left arrow key on a standard keyboard. If one opens a text editor and types
the keys abicdeweeef, the result is faecdb. We say that a s
Barycentric Coordinates for the Impatient
Max Schindler
Evan Chen
July 13, 2012
I suppose it is tempting, if the only tool you have is a
hammer, to treat everything as if it were a nail.
1
Introductio
Spring 2014 Executive Report
or: How to Write an OMO
Evan Chen
November 2013 - April 2014
This is some documentation about the process of preparing the 2014 Spring Online
Math Open. It is intended to
Expected Uses of Probability
Evan Chen
August 11, 2014
Sorry for the bad title. This is mostly about expected value, both in its
own right and in the context of the probabilistic method.
1 Definitions
Summations
Evan Chen
October 13, 2016
Mathematicians just love sigma notation for two reasons. First, it provides a convenient
way to express a long or even infinite series. But even more important, i
Chinese Terminology Sheet
Evan Chen
March 8, 2017
Chinese terminology sheet initially compiled as part of preparation for the
Taiwan IMO 2014 camps, but later expanded. There are likely many typos.
Pl
The Chinese Remainder Theorem
Evan Chen
February 3, 2015
The Chinese Remainder Theorem is a theorem only in that it is useful and requires
proof. When you ask a capable 15-year-old why an arithmetic p
A Brief Introduction to Olympiad Inequalities
Evan Chen
April 30, 2014
The goal of this document is to provide a easier introduction to olympiad
inequalities than the standard exposition Olympiad Ineq
Introduction to Functional Equations
Evan Chen
October 18, 2016
So have you ever played three-player bughouse chess and been on the middle board?
Basically, a very effective strategy is to just throw
18th Elmo Lives Mostly Outside
ELMO 2016
Pittsburgh, PA
OFFICIAL SOLUTIONS
1. Cookie Monster says a positive integer n is crunchy if there exist 2n real numbers
x1 , x2 , . . . , x2n , not all equal,
Monsters
Evan Chen
October 2, 2016
Whoever fights monsters should see to it that in the process he does not become a
monster. And if you gaze long enough into an abyss, the abyss will gaze back into y
Supersums of Square-Weights: A Dumbasss Perspective
Evan Chen
chen.evan6@gmail.com
January 6, 2013
The intended audience should already familiar with Muirhead and Schur
3
b3
c3
(e.g. the inequality ab
How to Use Directed Angles
Evan Chen
May 31, 2015
WLOG, diagram as shown. Everyone
This is a very brief note on what a directed angle is and how to use it to write olympiad
solutions which are impervi
Lagrange Murderpliers Done Correctly
Evan Chen
June 8, 2014
The aim of this handout is to provide a mathematically complete treatise
on Lagrange Multipliers and how to apply them on optimization probl
16th Ego Loss May Occur
ELMO 2014
Lincoln, Nebraska
OFFICIAL SOLUTIONS
1.
Find all triples (f, g, h) of injective functions from the set of real numbers to itself satisfying
f (x + f (y) = g(x) + h(y)
Solutions to TSTST 2015
United States of America
57th IMO 2016, Hong Kong
1 Solution to TSTST Problem 1
This problem was proposed by Mark Sellke.
Define
M (k) = max (ak + ak+1 + + ak+`1 ),
1`m
and let
15th Everyone Lives at Most Once
ELMO 2013
Lincoln, Nebraska
OFFICIAL SOLUTIONS
1.
Let a1 , a2 , . . . , a9 be nine real numbers, not necessarily distinct, with average m. Let A denote
the number of t
Remarks on English
MOP 2016 at Pittsburgh, PA
Evan Chen
June 8, 2016
Exposition, criticism, appreciation, is work for second-rate minds.
G. H. Hardy
1 Grading
Your score on an olympiad problem is a n
Solutions to USA(J)MO 2016
Evan Chen
57th IMO 2016, Hong Kong
1 Solution to JMO1
This problem was proposed by Ivan Borsenco and Zuming Feng.
Let M be the midpoint of arc BC not containing A. We claim
USA Team Selection Test for IMO 2015
Problems and Solutions
56th IMO 2015 at Chiang Mai, Thailand
1
Problems
Thursday, December 11, 2014
1. Let ABC be a non-isosceles triangle with incenter I whose in
37th English Language Masters Open
1. Let ABCD be a convex quadralateral. Let E, F, G, H be points on segments AB, BC,
CD, DA, respectively, and let P be intersection of EG and F H. Given that quadril
Solutions to December and January Team Selection Tests
United States of America
57th IMO 2016, Hong Kong
1 Solution to December TST, Problem 1
This problem was proposed by Maria Monks Gillespie.
Let u
Solutions to the 2016 TST Selection Test
Evan Chen
July 4, 2016
1 Solution to TSTST 1, proposed by Victor Wang
This is essentially an application of the division algorithm, but the details require
sig
English Language Masters Open
Day I
8:00 AM 12:30 PM
June 18, 2011
Write your number and team abbreviation, but not your name, on top of all pages turned in.
1. Let ABCD be a convex quadralateral. Let
Exceedingly Luck-based Math Olympiad
Day 1
1. Determine all (not necessarily finite) sets S of points in the plane such that given any
four distinct points in S, there is a circle passing through all