{"id":11364,"date":"2021-11-24T08:34:33","date_gmt":"2021-11-24T13:34:33","guid":{"rendered":"https:\/\/notes.math.ca\/?post_type=article&#038;p=11364"},"modified":"2022-02-06T20:29:43","modified_gmt":"2022-02-07T01:29:43","slug":"book-review-2","status":"publish","type":"article","link":"https:\/\/notes.math.ca\/en\/article\/book-review-2\/","title":{"rendered":"Book Review"},"content":{"rendered":"<p>Book<em> Reviews bring interesting mathematical sciences and education publications drawn from across the entire spectrum of mathematics to the attention of the CMS readership. Comments, suggestions, and submissions are welcome.<\/em><\/p>\n<p><strong>Karl Dilcher,&nbsp;<\/strong><em>Dalhousie University (<a href=\"mailto:notes-reviews@cms.math.ca\">notes-reviews@cms.math.ca<\/a>)<\/em><\/p>\n<p><a href=\"https:\/\/notes.math.ca\/wp-content\/uploads\/2021\/11\/winkler-cover.jpg\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/notes.math.ca\/wp-content\/uploads\/2021\/11\/winkler-cover-194x300.jpg\" alt=\"\" width=\"194\" height=\"300\"><\/a><b>Mathematical Puzzles<\/b><br \/>\nby Peter Winkler<br \/>\nA K Peters\/CRC Press, 2021<br \/>\nISBN:&nbsp;978-0367206925<br \/>\nReviewed by David Wolfe, Verisk Analytics<\/p>\n<p>I wished I\u2019d refused the assignment to review Peter Winkler\u2019s Mathematical Puzzles.&nbsp; As a reviewer, I felt compelled to read the puzzles and the solutions, but I was too addicted to the puzzles to <em>want<\/em> to see the solution to a tantalizing puzzle I had yet to solve.&nbsp; This is the greatest collection of puzzles I\u2019ve encountered, and is excellent reading for all ages of mathematically minded individuals from teenagers through experienced researchers.&nbsp; Whoever you are, do not expect to solve them all!<\/p>\n<p>Peter Winkler\u2019s excellent taste in puzzles comes through in both his selection and his presentation.&nbsp; Many puzzles are framed in a mini-story with captivating language or characters; and there are a few non-mathematical teasers thrown in.&nbsp; They include old classics like, \u201cBrothers and sisters I have none, but that man\u2019s brother is my father\u2019s son,\u201d and \u201cHow can you get a 50-50 decision by flipping a bent coin?\u201d&nbsp; But the real attraction for me was the number of puzzles from the last decade or two which are sure-to-be classics.<\/p>\n<p>Like many of Peter Winkler\u2019s own creations, this pair of puzzles spread through the mathematical community like wildfire:<\/p>\n<ul>\n<li>Alice and Bob each have $100 and a biased coin that comes up heads with probability 51%.&nbsp; At a signal, each begins flipping his or her coin once a minute and bets $1 (at even odds) on each outcome, against a bank with unlimited funds.&nbsp; Alice bets on heads, Bob on tails.&nbsp; Suppose both eventually go broke.&nbsp; Who is more likely to have gone broke first?\u201d<\/li>\n<li>Suppose now that Alice and Bob are flipping the same coin, so that when one goes broke, the second one\u2019s stack will be $200 [but will keep playing].&nbsp; Same question: Given that they both go broke, who is more likely to have gone broke first?\u201d<\/li>\n<\/ul>\n<p>Of course, since Winkler poses both questions, you can correctly infer that the answers differ!<\/p>\n<p>Winkler\u2019s choice of organization is a bit unusual.&nbsp; The puzzles are enumerated 4 times.&nbsp; The first lists the puzzles in an order that doesn\u2019t divulge the technique of solution.&nbsp;&nbsp; The second section of the book gives hints.&nbsp; The third, and largest, section of the book provides solutions to all the puzzles grouped by technique used; each of these sections ends with a well-chosen <em>bonus<\/em> theorem related to the technique.&nbsp; In the closing portion of the book, Peter Winkler describes what he knows of each puzzle\u2019s source or history.<\/p>\n<p>Most who pick up the book will no doubt want to work the puzzles as initially presented in the lead section.&nbsp; The first puzzles are easiest, but are plenty interesting and fun.&nbsp; Otherwise, they are well-mixed in both style and mathematical methods required.&nbsp; If, on the other hand, you are a person who prefers to use the book to study techniques, you may choose to jump straight into the third presentation of the puzzles.&nbsp; Each puzzle is repeated verbatim from the first section, so the solutions stand on their own.&nbsp; And the puzzles are sorted by difficulty, so the reader can build confidence in using the technique and stop when the waters get too deep.&nbsp; Each technique-specific chapter ends with a bonus theorem, one which is just the sort of theorem I might not have seen before but which I sure wish I knew years ago.<\/p>\n<p>Thank you, Peter, for assembling this magnificent potpourri!<\/p>\n<p><em>David Wolfe is co-author of several books on combinatorial game theory, most recently of the second edition of &#8220;Lessons in Play: An Introduction to Combinatorial Game Theory&#8221; (with Michael H. Albert and Richard J. Nowakowski), A K Peters\/CRC Press, 2019.<\/em><\/p>\n","protected":false},"author":6,"template":"","section":[25],"keyword":[],"class_list":["post-11364","article","type-article","status-publish","hentry","section-book-reviews"],"toolset-meta":{"author-4-info":{"author-4-surname":{"type":"textfield","raw":""},"author-4-given-names":{"type":"textfield","raw":""},"author-4-honorific":{"type":"textfield","raw":""},"author-4-institution":{"type":"textfield","raw":""},"author-4-email":{"type":"email","raw":""},"author-4-cms-role":{"type":"textfield","raw":""}},"author-3-info":{"author-3-surname":{"type":"textfield","raw":""},"author-3-given-names":{"type":"textfield","raw":""},"author-3-honorific":{"type":"textfield","raw":""},"author-3-institution":{"type":"textfield","raw":""},"author-3-email":{"type":"email","raw":""},"author-3-cms-role":{"type":"textfield","raw":""}},"author-2-info":{"author-2-surname":{"type":"textfield","raw":""},"author-2-given-names":{"type":"textfield","raw":""},"author-2-honorific":{"type":"textfield","raw":""},"author-2-institution":{"type":"textfield","raw":""},"author-2-email":{"type":"email","raw":""},"author-2-cms-role":{"type":"textfield","raw":""}},"author-info":{"author-surname":{"type":"textfield","raw":""},"author-given-names":{"type":"textfield","raw":""},"author-honorific":{"type":"textfield","raw":""},"author-email":{"type":"email","raw":"davidgameswolfe+cms@gmail.com"},"author-institution":{"type":"textfield","raw":""},"author-cms-role":{"type":"textfield","raw":""}},"unknown":{"downloadable-pdf":{"type":"file","raw":"https:\/\/notes.math.ca\/wp-content\/uploads\/2021\/11\/BookReview-CMSNotes-dec2021.pdf","attachment_id":11553},"article-toc-weight":{"type":"numeric","raw":"30"},"author-surname":{"type":"textfield","raw":""},"author-given-names":{"type":"textfield","raw":""}}},"_links":{"self":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/11364","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article"}],"about":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":5,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/11364\/revisions"}],"predecessor-version":[{"id":11375,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/11364\/revisions\/11375"}],"wp:attachment":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/media?parent=11364"}],"wp:term":[{"taxonomy":"section","embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/section?post=11364"},{"taxonomy":"keyword","embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/keyword?post=11364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}