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

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

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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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Contents
Problem Solving in Mathematics and Beyond Print ISSN 2591-7234 - photo 1

Problem Solving in Mathematics and Beyond Print ISSN 2591-7234 Online - photo 2

Problem Solving in Mathematics and Beyond

Print ISSN: 2591-7234
Online ISSN: 2591-7242

Series Editor:Dr. Alfred S. Posamentier
Distinguished Lecturer
New York City College of Technology - City University of New York

There are countless applications that would be considered problem solving in mathematics and beyond. One could even argue that most of mathematics in one way or another involves solving problems. However, this series is intended to be of interest to the general audience with the sole purpose of demonstrating the power and beauty of mathematics through clever problem-solving experiences.

Each of the books will be aimed at the general audience, which implies that the writing level will be such that it will not engulfed in technical language rather the language will be simple everyday language so that the focus can remain on the content and not be distracted by unnecessarily sophiscated language. Again, the primary purpose of this series is to approach the topic of mathematics problem-solving in a most appealing and attractive way in order to win more of the general public to appreciate his most important subject rather than to fear it. At the same time we expect that professionals in the scientific community will also find these books attractive, as they will provide many entertaining surprises for the unsuspecting read er.

Published

Vol. 16 Mathematical Muffin Morsels: Wants a Small Piece
by William Gasarch, Erik Metz, Jacob Prinz and Daniel Smolyak

Vol. 15 Teaching Secondary School Mathematics: Techniques and Enrichment
by Alfred S Posamentier and Beverly Smith

Vol. 14 Engaging Young Students in Mathematics through Competitions Perspectives and Practices: Volume II Mathematics Competitions and how they relate to Research, Teaching and Motivation; Entertaining and Informative Papers from the WFNMC8 Congress in Semriach/Austria 2018
edited by Robert Geretschlger

Vol. 13 Engaging Young Students in Mathematics through Competitions World Perspectives and Practices: Volume I Competition-ready Mathematics; Entertaining and Informative Problems from the WFNMC8 Congress in Semriach/Austria 2018
edited by Robert Geretschlger

For the complete list of volumes in this series, please visit www.worldscientific.com/series/psmb

Published by World Scientific Publishing Co Pte Ltd 5 Toh Tuck Link - photo 3

Published by

World Scientific Publishing Co. Pte. Ltd.

5 Toh Tuck Link, Singapore 596224

USA office:27 Warren Street, Suite 401-402, Hackensack, NJ 07601

UK office:57 Shelton Street, Covent Garden, London WC2H 9HE

Library of Congress Cataloging-in-Publication Data

Names: Gasarch, William I., author. | Metz, Erik, author. | Prinz, Jacob, author. | Smolyak, Daniel, author.

Title: Mathematical muffin morsels : nobody wants a small piece / William Gasarch (University of Maryland, USA), Erik Metz (University of Maryland, USA), Jacob Prinz (University of Maryland, USA) and Daniel Smolyak (University of Maryland, USA).

Description: New Jersey : World Scientific, [2020] | Series: Problem solving in mathematics and beyond, 2591-7234 ; vol. 16 | Includes bibliographical references and index.

Identifiers: LCCN 2020007589 | ISBN 9789811215179 (hardcover) | ISBN 9789811215971 (paperback) | ISBN 9789811215186 (ebook) | ISBN 9789811215193 (ebook other)

Subjects: LCSH: Mathematics--Problems, exercises, etc. | Division--Problems, exercises, etc. | Fractions--Problems, exercises, etc.

Classification: LCC QA43 .G347 2020 | DDC 513.2/1--dc23

LC record available at https://lccn.loc.gov/2020007589

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Copyright 2020 by World Scientific Publishing Co. Pte. Ltd.

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