000			a
999			_c32470 _d32470
008			230831b xxu||||| |||| 00| 0 eng d
020			_a9789811215971
082			_a513.21 _bGAS
100			_aGasarch, William I.
245			_aMathematical muffin morsels : nobody wants a small piece
260			_bWorld Scientific, _c2020 _aNew Jersey :
300			_axvi, 210 p. ; _bill., (some color), _c24 cm
365			_b28.00 _cUSD _d85.40
490			_aProblem solving in mathematics and beyond, _v2591-7234 ; v.16
504			_aIncludes bibliographical references and index.
520			_aSuppose 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.
650			_aBuddy-match sequence
650			_aDuality theorem
650			_aFair divisions
650			_aLinear programming
650			_aMixed integer programming
650			_a NP-complete
650			_aPigeon Hole Principle
650			_aSimplex method
650			_aCombinatorics
650			_aOptimization theory
700			_aMetz, Erik
700			_aPrinz, Jacob
700			_aSmolyak, Daniel
942			_2ddc _cBK