Winners of the highest prize in mathematics, the Fields Medal, were announced last week. Presented every four years to four mathematicians under the age of 40, the award recognizes both outstanding work and future promise
Among the 2022 medalists, 37-year-old Marina Vyazovskaya from Ukraine won for her pioneering work on how to pack spheres in 24 dimensions.
In her honor, today’s first puzzle is about how to package beer in three dimensions.
1. The drawer problem
Can you fit more than 40 beer cans that are 1 unit in diameter and 2.6 units in height in a 5 x 8 x 2.6 crate?
James Maynard, 35, of Great Britain, won the 2022 Fields Medal for his many simple results about prime numbers. As a tribute to his success, here is a puzzle about the number 13, a simple number.
2. Armchairs, comrade.
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.
Jun Hu, 39 years old from the USA, won for results that connect graph theory, combinatorics, algebra, and many other abstract concepts. A graph in this context means a network of individual points connected to each other, which is one way of thinking about a chessboard, which is 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). A different person stands on each square. Can all 81 people go to the next square so that there is a different person on each square again?
36-year-old Hugo Duminil-Coppin from France received the medal for his work on phase transitions in statistical physics. I couldn’t find a simple riddle about this area. If any readers have any suggestions, please put them in the comments below.
I’ll be back at 5pm UK with the answers.
Meanwhile, NO SPOILERS!
Finally, if you enjoy this column, you can buy the Guardian in newspaper form on Saturday (July 16). I edited the 16 page Summer puzzle supplement that will be free with the paper. It features puzzles from around the world, including sudoku hand-crafted by our friends 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 number of guides on how to solve the riddles. Don’t miss it!
I post a puzzle here every two weeks on Monday. I’m always on the lookout for great puzzles. If you want to suggest one, write to me.
I am the author of several puzzle books, as well as the School of Soccer series of children’s books. last installment The greatest book of quizzes, just came out.
I give school talks about maths and puzzles (online and in person). If your school is interested, please contact