ENGLISH

Mathematical Muffin Morsels: Nobody Wants A Small Piece: 16 (Problem Solving in Mathematics and Beyond)

By William Gasarch , Erik Metz , Jacob Prinz , Daniel Smolyak

Book information

Publisher
World Scientific Publishing Company
Year
2020
ISBN
2020007589, 9789811215179, 9789811215971, 9789811215186, 9789811215193, 9811215170
Language
english
Format
EPUB
Filesize
16 MB (16719812 bytes)
Pages
250\0
Library
Mobilism
Time added
2021-10-21 04:31:08

Description

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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