<p>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.</p><p>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.</p><p>In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up <em>m</em> muffins for <em>s</em> students so that everyone gets <em>m</em>/<em>s</em> muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.</p><p>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.</p>