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Simple Sequence Stumps the World’s Best (IMO 2024 Problem 3)

Here’s a nice way to understand it 🥰

Russell Lim
Nice Math Problems
11 min readAug 6, 2024

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A simple sequence…

Here is a fascinating sequences problem from this year’s IMO (International Mathematical Olympiad).

It was Problem 3, which is the final problem on Day 1. Usually I would not even attempt an IMO Problem 3, as they are designed to challenge mathematicians far above my level.

But when I read this problem statement I was enticed by its simplicity…

source: https://www.imo2024.uk/

Each term is just equal to the number of times the previous term has appeared in the list.

Furthermore, when I read that this problem was proposed by an Australian mathematician (my home country), I was hooked. 🎣

I started trying some examples, first by hand and then with a computer, seeing if I could understand why the sequence always becomes periodic. On the one hand it seemed so obvious and natural, but on the other hand so difficult to prove. After thinking about this problem on and off for almost a week, I’m ready to explain how it works. 💪

Here goes…

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Nice Math Problems
Nice Math Problems

Published in Nice Math Problems

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Russell Lim
Russell Lim

Written by Russell Lim

I teach high school mathematics in Melbourne, Australia. I like thinking about interesting problems and learning new things.

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