Can you solve it? Fields Medals for Beginners | Math

The winners of the most prestigious prize in mathematics, the Fields Medal, were announced last week. The award, which recognizes up to four mathematicians under the age of 40 every four years, is recognition of both outstanding work and future promise.

Among the 2022 medalists, 37-year-old Marina Viazovska from Ukraine won for her groundbreaking work on how to pack 24-dimensional spheres.

In his honor, today’s first riddle is about how to wrap beers in three dimensions.

1. A checkout 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 box with dimensions 5 x 8 x 2.6?

James Maynard, 35, of the United Kingdom, won a 2022 Fields Medal for his numerous prime results. In tribute to its success, here is a puzzle around the number 13, a prime number.

2. Chairs, man.

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 United States, won for her results linking graph theory, combinatorics, algebra and many other abstract concepts. A graph in this context means a network of discrete dots connected to each other, which is a way of thinking of a chessboard, which is made up of discrete squares connected to each other.

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 standing on it. Is it possible for all 81 people to walk to a neighboring square, so that each square again has a different person on it?

Hugo Duminil-Copin, 36, of French nationality, won a medal for his work on phase transitions in statistical physics. I couldn’t find a simple riddle on this area. If any readers can suggest one, please put it in the comments below.

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

In the meantime NO SPOILERS!

Finally, if you like 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 which will be free with the paper. It features puzzles from around the world, including hand-crafted sudoku by our friends at Cracking the Cryptic, all-new Japanese logic grid puzzles, a selection of Grabarchuk family teasers, many types of word puzzles and several crosswords, including a guide of how to solve the puzzles. Don’t miss it!

I install a puzzle here every two weeks on a Monday. I’m always on the lookout for great puzzles. If you want to suggest one, write to me.

I’m the author of several puzzle books, as well as the Football School children’s book series. The last payment, The greatest quiz book of all time, just got out.

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