Split a Cake Between Two People So Neither One Complains
Two people want to share a cake, but neither trusts the other to cut it fairly, and there's no outside referee to measure exact halves. Neither has to value every part of the cake the same way — one might prize the frosting, the other the fruit filling. Design a simple procedure, using only the two of them, that guarantees neither person ever feels shortchanged, no matter how each one privately values the pieces.
Reveal the answer
Have one person cut the cake into what they consider two equal halves, then let the other person choose whichever half they want — the cutter has no reason to cut unevenly since they don't know which piece they'll get, and the chooser is guaranteed the piece they value at least as much. Known as 'divide and choose,' versions of this rule appear in ancient Greek and Hebrew sources, and it was rigorously formalized in the 1940s by mathematicians Hugo Steinhaus, Stefan Banach and Bronisław Knaster, launching the mathematical field of fair division.