Mathematical muffin morsels: nobody wants a small piece
"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 th...
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
[2020]
|
| Schriftenreihe: | Problem solving in mathematics and beyond
v. 16 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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 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"--Publisher's website |
| Beschreibung: | 1 Online-Ressource (xvi, 210 Seiten) |
| ISBN: | 9789811215186 9811215189 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:30:25Z |
| indexdate | 2024-07-10T09:03:18Z |
| institution | BVB |
| isbn | 9789811215186 9811215189 |
| language | English |
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| spelling | Mathematical muffin morsels nobody wants a small piece by William Gasarch... [et al.] Singapore World Scientific [2020] 1 Online-Ressource (xvi, 210 Seiten) txt rdacontent c rdamedia cr rdacarrier Problem solving in mathematics and beyond v. 16 "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 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"--Publisher's website Mathematics / Problems, exercises, etc Division / Problems, exercises, etc Fractions / Problems, exercises, etc Gasarch, William I. Sonstige oth https://www.worldscientific.com/worldscibooks/10.1142/11689#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mathematical muffin morsels nobody wants a small piece Mathematics / Problems, exercises, etc Division / Problems, exercises, etc Fractions / Problems, exercises, etc |
| title | Mathematical muffin morsels nobody wants a small piece |
| title_auth | Mathematical muffin morsels nobody wants a small piece |
| title_exact_search | Mathematical muffin morsels nobody wants a small piece |
| title_exact_search_txtP | Mathematical muffin morsels nobody wants a small piece |
| title_full | Mathematical muffin morsels nobody wants a small piece by William Gasarch... [et al.] |
| title_fullStr | Mathematical muffin morsels nobody wants a small piece by William Gasarch... [et al.] |
| title_full_unstemmed | Mathematical muffin morsels nobody wants a small piece by William Gasarch... [et al.] |
| title_short | Mathematical muffin morsels |
| title_sort | mathematical muffin morsels nobody wants a small piece |
| title_sub | nobody wants a small piece |
| topic | Mathematics / Problems, exercises, etc Division / Problems, exercises, etc Fractions / Problems, exercises, etc |
| topic_facet | Mathematics / Problems, exercises, etc Division / Problems, exercises, etc Fractions / Problems, exercises, etc |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11689#t=toc |
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