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

Note by Michael Ng
3 years, 9 months ago

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1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. 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"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

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BRILLIANT\huge\huge{BRILLIANT} , when will the problems be posted.

Shivam Jadhav - 3 years, 9 months ago

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I have posted the first one; I really liked this problem! Hope you enjoy it too!

Michael Ng - 3 years, 9 months ago

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Great!!!!!

shivam mishra - 3 years, 9 months ago

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Thanks a lot flor share these problems

Fernando Sánchez - 3 years, 9 months ago

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I too did participate in IMO

Ashish Siva - 3 years, 9 months ago

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Really?

Nihar Mahajan - 3 years, 7 months ago

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I guess he meant SOF :)

A Former Brilliant Member - 3 years, 7 months ago

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@A Former Brilliant Member Yes SOF

Ashish Siva - 3 years, 7 months ago

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Yes, but private schools

Ashish Siva - 3 years, 7 months ago

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@Ashish Siva Thank God! I thought you participated in REAL IMO.

Nihar Mahajan - 3 years, 7 months ago

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