The Liar Paradox and the Towers of Hanoi: The 10 Greatest Math Puzzles of All Time

by Marcel Danesi

Book Overview

A walk through history's most mind-boggling puzzles
Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused. The Liar Paradox and the Towers of Hanoi takes die-hard puzzle mavens on a tour of the world's most enduringly intriguing braintwisters, from K?nigsberg's Bridges and the Hanoi Towers to Fibonacci's Rabbits, the Four Color Problem, and the Magic...

• Format: Paperback
• Language: English
• ISBN: 0471648167
• ISBN13: 9780471648161
• Release Date: August 2004
• Publisher: Trade Paper Press
• Length: 248 Pages
• Weight: 0.74 lbs.
• Dimensions: 0.7" x 6.1" x 9.3"

Customer Reviews

Why this universal fascination with puzzles?

I have been fascinated with puzzles ever since my teens;which is now over 60 years ago.The term "puzzles" covers such a field,that I was really impressed with this book.When I first started,the first puzzle I came across was "The 15 Puzzle;then later "The Towers of Hanoi".And that was only the start of what became a lifelong interest in searching for new puzzles and books on puzzles. Although the reason the author set upon writing this book was to explain the association of ,and the mathematics involved ,with puzzles;he also did something else at the same time.He shows what the whole world of Puzzles and Mathetical Recreations is all about by taking what he calls "The Ten Greatest Math Puzzles of All Times",explaining them,then expanding on them to show how so many other puzzles stem from them.I have collected somewhere between 6 and 7 hundred puzzle books over the years,many of which the author references,and I have to say,that this book does as good as any I have ever come across ,in explaining what the whole fascination of "Recreational Mathematics" is all about. It was eye opening years ago to find good books on this subject,even harder to find puzzles.Jigsaw and Crossword were common,but little else.Then I found Mathematical Games in "Scientific American;"which led me to many other things.Now,with the "Net" the whole world of Puzzles and books of Puzzles and Mathematical Recreations opens up a pletora of things for the puzzler. This book has something for everyone,whether it is Riddles,Paradoxes,River-Crossing Puzzles,Map Coloring Problems,Optical Illusions,Mazes,Magic Squares,etc.,a neophyte or someone who has been interested in puzzles for years;will find lots new and interesting here.As an example,I became fascinated with Magic Squares while in University.I learned a method to complete any odd-order Magic Square;but try as I may,I could never "crack" even-order ones.I asked the head of the Math Department if he ever tried. A few days later he handed me notes on how to do it--I was thrilled.I was thrilled once again when in this book ,what did I find but a Magic Cube!! Although this is an excellent book in all respects and will give anyone interested in puzzles a lot of enjoyment,and there are along with everything else, 72 challenging puzzles with detailed answers,all kinds of related references for further reading,and a good Glossary;there are two things I would like to mention.For many years ,it was believed that Sam Loyd invented the "15 Puzzle";and it is stated so here in 2004.Jerry Slocum and Dic Sonneveld wrote an excellent book,"The 15 Puzzle" in 2006 which proved that Sam Loyd didn't invent it after all. That just goes to show there's always something new in puzzles.The other comment I have ,is that I'm surprised that the Tanram was not chosen as one of the "greatest". However,with so many to choose from;it's almost like trying to pick the greatest song or the greatest of anything;but I must admit;the authors choice i

For a mixed audience

I think this book aims at a mixed audience with mixed success. For the puzzle solver, there is interesting background on some popular forms, but probably not enough puzzles. For someone with a background in math the exploration is too simple, (e.g. one paragraph of Godel) and for the computer scientist not enough exploration of algorithms. For the historian of science there are some new perspectives, but the history is not carried through. On the discussion of Labyrinths, I wish Danesi would have mentioned the book Labyrinths by Borge, and also alluded to the form in some churches. Although the book may not be for the "specialist", there is quite a bit of fun for anyone here. For example I had been familiar with the Fibonacci series, but hadn't seen the Rabbit Puzzle before. Everyone has heard of the Mobius strip, but the Klein bottle was new to me (and I'd love to buy one). I had done mazes before, but the one by Lewis Carroll us fun.

Good start, but never becomes really challenging

Liar's Paradox has ten chapters covering 10 puzzles that mankind has created over its history. Each chapter covers a main puzzle, the historical and philosophical background behind it, and describes how each affected mathematics/science as people thought their way through the puzzles. Each chapter includes a set of follow up questions/puzzles, with a good answer section at the back. One should note that while most of the chapters focus on math, others seem only indirectly related--for instance, one chapter is almost solely devoted to problems related to perception and psychology (such as two-tone pictures in which you can see both a vase and two people's faces), and other chapters are related to math only in extremely advanced ways--for instance, the Liar's Paradox may be a math problem for some, but at the level this book is written it doesn't really get past a discussion of logical paradoxes. On that note, this book is written at the level of someone who vaguely remembers high school algebra (for instance, there is a fairly in depth discussion of what "exponents" are). For someone at that level, I think the book is excellent. The puzzles Mr. Danesi chooses are interesting and all described well. The puzzles at the end of each chapter are entertaining. I think readers should recognize before they buy this book that it is probably not meant to be a brain-wracking, headache-inducing puzzle book, but rather a leasurely review of some of mankind's more interesting puzzles. Mr. Danesi has done a good job of accomplishing that.