Can you solve it? The Fields Medals for Beginners | Math

Last week, the winners of the most high-profile math award, the Fields Medal, were announced. The prize, awarded every four years to up to four mathematicians under the age of 40, recognizes both outstanding work and future promise.

Of the 2022 medalists, Maryna Viazovska, age 37, from Ukraine, won for her groundbreaking work on packaging spheres in 24 dimensions.

In her honor, today’s first puzzle is about three-dimensional packaging of beers.

1. A Crate Problem

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

Here are 40 in the box. But can you fit even more into it?

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

2. Chairs, mate.

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

June Huh, 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 together, which is one way you might think of a chessboard, which is discrete squares connected together.

3. Chess Neighbors

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

Hugo Duminil-Copin, 36 years old, from France, won a medal for his work on phase transitions in statistical physics. I couldn’t find a simple puzzle about this area. If readers can suggest one, please post it in the comments below.

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

Meanwhile NO SPOILERS!

UPDATE: You can now read the solutions here

Finally, if you enjoy this column, you may want to buy the Guardian on Saturday (July 16) in newspaper form. I’ve edited a 16-page Summer Puzzle Supplement that will be free with the paper. It features puzzles from around the world, including handcrafted sudokus from our friends at Cracking the Cryptic, brand new Japanese logic grid puzzles, a selection of Grabarchuk family teasers, many different types of word puzzles and various crossword puzzles, including a guide to how to solve cryptic solutions on to solve. Do not miss it!

I put a puzzle here every two weeks on Mondays. I am always looking for great puzzles. If you’d like to suggest one, drop me an email.

I am the author of several puzzle books and also the Football School children’s book series. the last episode, The greatest quiz book ever just came out.

I give school lectures on math and puzzles (online and in person). If your school is interested, please contact us.

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