In his session about “What is mathematical proof?” on Monday 3 November Tim Gowers will mention the 15-puzzle.
This is a puzzle which was invented in the 1870s, became an international craze in the 1880s, and is widely available as a computer app today.
You have 15 tiles in a 16-square box, for example:
The puzzle is to shift them around, using the empty square, so that you get them into the right order:
The maths of the 15-puzzle brings in some powerful and widely-used ideas, such as odd and even permutations.