IMO Training: Set 1 Introduction

Almost every secondary school mathematician aspires to participate in the internationally acclaimed competition that is the IMO (International Mathematical Olympiad).

The problems are usually incredibly challenging, and whilst many are perfectly possible without any prior knowledge, knowing certain techniques or theorems can be extremely helpful. Sometimes it can even trivialise the easier problems!

This set of 12 problems is intended to put many of those techniques in one place. All of them are ones that I have found to be beautiful, and I hope that you will enjoy them too! They will be slight adaptations from those in the IMO Shortlist (not only for a little variation, but also to prevent easy cheating), but the solutions will demonstrate the original technique used in the problem. I will only be using problems that can be easily adapted to give a numerical answer to suit the Brilliant answer submission system. Here is a link to the set.

I will be posting these problems on a semi-regular basis. Also most importantly, I do not take the credit for creating any of these problems nor for finding most of these beautiful solutions; I just want more people on Brilliant to enjoy doing them!

Best, Michael

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

IMO Training: Set 1 Introduction

Comments