The most important event in the mathematical calendar will be held in St Petersburg. The Fields Medal, the most prestigious prize in mathematics, is announced at the International Congress of Mathematicians, which is a quadrennial gathering.
The online competition for students and the general public was part of the build-up to the event, which is expected to attract about 5,000 mathematicians from all over the world. The first three questions are from the test.
Russia has long been a leader in mathematics outreach, having pioneered the idea of maths circles and competitive mathematics olympiads.
The Russian style of puzzles tests logical reasoning rather than teaching mathematical skills. The first one is a classic.
1. Pet swap.
A cat is sitting on a table and a tortoise is crawling on the floor. The cat has a distance from its ears to the top of the tortoise's shell. Alena had pets. The cat has a distance from its ears to the top of the tortoise's shell. What is the height of the table?
The illustration is for ICM 2022.
2. Circular thinking.
Volodya is running around a track. Two points on the track have yellow marks on them. Volodya was close to the first yellow mark for 2 minutes, then he was close to the second yellow mark for 3 minutes, and then he was close to the first yellow mark again.
How long does it take Volodya to run a full circle?
3. The path of glory.
To walk through the 3x3 grid below left, you must move from cell to cell vertically or horizontally, and not enter any cell more than once. One path is shown below right. If she writes down the digits she passes in order, she will get the number 84937561.
The illustration is for ICM 2022.
What is the largest number that can be written down during a path through the grid?
I will be back in the UK at 5pm with the solutions. There are noSPOILERS.
I am grateful to the ICM for allowing me to use the puzzles. You can read more about the event here. The first source is the mathematics clubs folklore. 2. The Moscow Mathematics Olympiad was held in 2015. There was a math festival in 2012 I rephrased the questions to make them clearer.
I put a puzzle here on Mondays. I look for great puzzles. Email me if you would like to suggest one.
I give school talks about math and puzzles. Please contact your school if you are interested.
I have written several books of mathematics and puzzles, all of which would make great Christmas gifts.
