Can you solve it? The Fields medals for beginners

The winners of maths’ most high-profile prize, the Fields Medal, were announced last week. The award, which every four years goes to up to four mathematicians under 40, is a recognition both of outstanding work and future promise

Of the 2022 medallists, Marina Viazovska, aged 37, from Ukraine, won for her groundbreaking work on how to pack spheres in 24 dimensions.

In her honour, today’s first puzzle is about how to pack beers in three dimensions.

1. A crate problem

Is it possible to put more than 40 cans of beer of diameter 1 unit and height 2.6 units in a crate that has dimensions 5 x 8 x 2.6?

Here’s 40 in the crate. But can you fit any more in?

James Maynard, aged 35, from the UK, won a 2022 Fields Medal for his many prime results about prime numbers. As a tribute to his success, here is a puzzle about the number 13, a prime number.

2. Chairs, mate.

Place 13 chairs along the walls of a rectangular room such that each wall has the same number of chairs as the wall it faces.

June Huh, aged 39, from the US, won for results linking graph theory, combinatorics, algebra and many other abstract concepts. A graph in this context means a network of discrete points connected to each other, which is one way you might think of a chessboard, which is discrete squares connected to each other.

3. Chess neighbours

Imagine a 9×9 chessboard. (Like a Sudoku grid, but with alternating black and white cells). Each square has a different person standing on it. Is it possible for all 81 people to step onto a neighbouring square, so that each square again has a different person on it?

Hugo Duminil-Copin, aged 36, from France, won a medal for his work on phase transitions in statistical physics. I was unable to find a simple puzzle about this area. If any readers can suggest one please put it in the comments below.

I’ll be back at 5pm UK with the answers.

Meanwhile NO SPOILERS!

Lastly, if you enjoy this column, you might want to buy the Guardian in newspaper form on Saturday (July 16). I have edited a 16-page Summer puzzle supplement that will be free with the paper. It includes puzzles from around the world including hand-crafted sudoku by our pals at Cracking the Cryptic, brand new Japanese logic grid puzzles, a selection of teasers from the Grabarchuk family, many different types of word puzzles and several crosswords including a guide of how to solve cryptics. Don’t miss it!

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of puzzles, and also the children’s book series Football School. The latest instalment, The Greatest Ever Quiz Book, is just out.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.


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