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Mathematical Muffin Morsels: Nobody Wants a Small Piece - Hardcover
$93.96
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by Gasarch William (Author)
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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Standard U.S. returns are accepted for eligible new, unopened items within 30 days of carrier delivery. Returns are by mail. Customers are responsible for standard return shipping, there is no restocking fee, and standard exchanges are not offered. Once an approved return is received and inspected, the refund is issued to the original payment method within 5 business days. Damaged, defective, or incorrect items are handled at no return-shipping cost to the customer.
Return eligibility is subject to the full policy. Opened, read, or unsealed books with broken seals or visible wear are final sale. Digital downloads, gift cards, and personalized products are non-refundable. Original shipping charges are not refunded for standard returns. Contact us within 7 days of delivery about damaged, defective, or incorrect items.
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