In 1944, as the Russian army fought to reclaim Poland from the Germans, the mathematician Hugo Steinhaus, trapped in the city of Lvov, sought distraction in a puzzle. As you do.
The puzzle was this. Several people want to share a cake (by all means, replace that by a pizza if you wish). And, they want the procedure to be fair, in the sense that no one will feel that they have got less than their fair share.
Steinhaus knew that for two people there is a simple method: one person cuts the cake in two pieces, and the other chooses which one they want. The second person can’t complain, because they made the choice. The first person also can’t complain — if they do, it was their fault for cutting the cake wrongly.
How can three people divide a cake fairly?
Ref: Professor Ian Stewart’s Cabinet of Mathematical Curiosities
More fun coming,
Nalin Pithwa
Mathematics Hothouse 