The most important and important event of the mathematical calendar will take place next July in St. Petersburg. The International Congress of Mathematicians is a quadrennial gathering at which many of the subject’s most eminent thinkers lecture and the winners of mathematics’ most prestigious award, the Fields Medal, are announced.

As part of the preparation for the event – which is expected to attract around 5,000 mathematicians from around the world – organizers earlier this year held an online math competition for students and the general public. Below are the first three questions for this test.

Russia has long been a world leader in spreading mathematics, having initiated the idea of ​​math circles (informal math clubs where students often try to solve problems in groups) and competitive math Olympiads.

Today’s three puzzles are all shining examples of the Russian style: they test logical reasoning rather than teaching math skills. The first, in particular, is a classic.

1. Animal exchange

A cat sits on the table and a turtle crawls on the ground just below. The distance from the cat’s ears to the top of the turtle’s shell is 170 cm. Alena changed her pets. Now the distance from the cat’s ears to the top of the turtle’s shell is 130cm. How high is the table?

Illustration: ICM 2022

2. Circular thinking

Volodya runs around a circular track at a constant speed. At two of the points on the track are two yellow marks. When he started his run, Volodya was closer to the first yellow mark for 2 minutes, then he was closer to the second yellow mark for 3 minutes, then he was closer to the first yellow mark again.

How long does it take Volodya to make a complete turn?

3. Path to Glory

Olga should walk the 3×3 grid at the bottom left, moving horizontally or vertically from cell to cell, and not enter any cell more than once. Below right shows a possible path. If Olga writes down the numbers she passes in order during this path, she will get the number 84937561.

ICM puzzle
Illustration: ICM 2022

What is the largest possible number that Olga can write on a run through the grid?

I’ll be back at 5pm in UK with the solutions. In the meantime, NO SPOILERS.

Thanks to ICM 2022 for allowing me to use the puzzles. You can find more about the event here. Sources: 1: Folklore of math clubs. 2. Moscow Mathematics Olympiad 2015 3. Math Fest 2012. I rephrased the questions for clarity.

LLPB paperback

I put a puzzle here every two weeks on a Monday. I am always on the lookout for great puzzles. If you would like to suggest one, send me an email.

I also give school lectures on mathematics and puzzles (restrictions permitting). If your school is interested, please contact us.

I have authored several math and puzzle books, most recently The language lovers puzzle book, all of which would make fantastic Christmas gifts!

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