Suppose you have five muffins that you want to divide and give to
Alice, Bob, and Carol. You want each of them to get 5/3. You could
cut each muffin into 1/3-1/3-1/3 and give each student five
1/3-sized pieces. But Alice objects! She has large hands! She wants
everyone to have pieces larger than 1/3.Is there a way to divide
five muffins for three students so that everyone gets 5/3, and all
pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a
division where the smallest piece is 5/12. Is there a better
division? Spoiler alert: No.In this book we consider THE MUFFIN
PROBLEM: what is the best way to divide up m muffins for s students
so that everyone gets m/s muffins, with the smallest pieces
maximized. We look at both procedures for the problem and proofs
that these procedures are optimal.This problem takes us through
much mathematics of interest, for example, combinatorics and
optimization theory. However, the math is elementary enough for an
advanced high school student.
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