The alphabetical order of numbers, the math enigma of “Le Monde” n° 23

On the eve of the Olympic Games, we were closing the first season of mathematical puzzles on the open problem of squaring the cube. It was a question of cutting a hollow cube into several pieces in order to be able to reconstruct a square. I proposed in particular to try to achieve this cutting with as few pieces as possible.

There were twenty-two of you who participated and you proposed a total of thirty-four different cuts. Two of you discovered cuts with four pieces! The one in figure A was discovered by Jérôme Petitjean and the one presented in figure B by Jérôme Roche. These two figures start from the same cube template before cutting it into four pieces.

Reading all your solutions, however, it seemed to me that it was a shame to only publish the proposals with the minimum number of pieces, because you were able to imagine a particularly astonishing diversity of methods. Figure C, for example, shows a solution designed by Rault Stanislas and using the cutting of Vesa Timonen’s miter that I presented to you in the enigma. By cutting the six faces of the cube in two diagonally, it is possible to easily reconstruct a miter on which it is then sufficient to reproduce the cutting discovered by Timonen at the beginning of the year. Doing maths often means knowing how to reduce yourself to a problem that you already know!

As the space I have in this section is limited, you can find a complete review of the solutions I received on the website of Monde.

Note, however, that to date, it has not been proven that we cannot do better. If you manage to find a solution in less than four pieces, or if you have proof that it is not possible, write to the email address [email protected]. I will not fail to keep you informed of future progress on the problem.

All this leaves me with a little bit of space to ask you a short riddle for next week. If we write the numbers in letters and put them in alphabetical order, “zero” will obviously come last. But which number will be first? And second? Third?

Find the previous puzzles by clicking here