Here’s a small puzzle that opens the door to a surprisingly tricky general problem: How can a teacher divide 24 muffins among 25 students so that everyone gets the same amount to eat but nobody gets stuck with any tiny pieces?

To get a clearer sense of what counts as a good answer, let’s consider a bad answer. You *could* remove 1/25th of each muffin, give an almost-complete muffin to each of the first 24 students, and give the 24 slivers to the last student. Then everyone gets 96% of a muffin, but it‘s a pretty crumby scheme for the student who gets nothing but slivers. We’d like to do better. Can you find a scheme in which the smallest piece anyone gets stuck with is bigger than 1/25 of a muffin? Can you find a solution in which the smallest piece is a *lot* bigger? After you’ve found the best solution you can and you can’t improve it, how might you try to prove that it’s the best solution anyone could ever find? And how would you solve the problem if there were a different number of muffins and/or a different number of students trying to share them? Puzzles of this kind can be challenging and addictive, and the general solution wasn’t found until last year.

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