What if one of those receiving a slice is the Lion? What most people don't realize is that "The Lion's Share" isn't the majority, or even "the vast majority", but *100%* !! http://www.aesopfables.com/cgi/aesop1.cgi?sel&TheLionsShare So, *zero* cuts suffice (although in the fable, the Lion has the dead stag quartered, but then proceeds to take all 4 quarters). Æsop. (Sixth century B.C.) Fables. The Harvard Classics. *1909–14*. [Just prior to the 16th "Income Tax" Amendment.] At 08:46 AM 12/15/2017, Michael Kleber wrote:

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