Talk 9/12: William Gasarch on the Muffin Problem

Let's say you have five muffins and you want to cut them up and give them out to Alice, Bob, and Carol so that they each get 5/3. This is easy, you can cut each one into thirds and give each person five 1/3-pieces.

But then the smallest piece is 1/3. Can we do better? Is there a way to divide five muffins for three people so that the smallest piece is BIGGER than 1/3? What is the BEST you can do? More generally: Given M muffins and P people, how can you divide m muffins so that each person gets M/P and the SMALLEST piece is MAXIMIZED?

Professor Gasarch will discuss various techniques to solve this problem and why this was a good research project.