Guy: What if after pie-spinning, Alice thinks she got the worst piece and would prefer either Bob's or Carol's, while Bob and Carol would each prefer Alice's? Then everyone is unhappy, but Alice gets to trade with someone, and Bob and Carol fight with each other over which one she trades with. Seems unsatisfying. --Michael On Fri, Dec 15, 2017 at 10:23 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
The problem is usually expressed as one of dividing a cake (or pie) and distributing it so that no-one is in a position to complain about the size of their slice ...
There's this ... https://www.scientificamerican.com/ article/the-mathematics-of-cake-cutting/
... and then there's this by Ian Stewart https://www.amazon.co.uk/How- Cut-Cake-Mathematical-Conundrums/dp/0199205906
However, the best solution I know of (which Ian Stewart confirmed he had not heard of) came from the 13-year-old son of a colleague of mine ....
Everyone gets a knife and makes a cut in a circular cake which is standing on a turntable ... with the aim of making equal-size slices.
The cake is then spun, and everyone gets the slice opposite them.
[ In other words, the randomness takes the decision about who gets what away from the hungry mathematicians ]
Guy
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