Title: Oval track and other permutation puzzles : and just enough group theory to solve them /
Authors: Kiltinen, John O.
Publisher: Published and distributed by the Mathematical Association of America Press,
Year: 2003
Subjects: Permutations.; Mathematical recreations.
Abstract: This book and the Permutation Puzzles Package of software that comes with it are the result of over ten years of development and classroom testing. The software presents the user with an array of computerized puzzles, plus tools to vary them in thousands of ways. The book provides the background needed to use the puzzle software to its fullest potential, and also gives the reader a gentle, not too technical introduction to just enough of the theory of permutation groups to fully understand how to solve puzzles of this type. The Oval Track Puzzles presented in the software have numbered disks which can be moved around an oval-shaped track, and a single "Do Arrows" button that allows for changing just a few of them. Have the computer scramble the numbers, and see if you can get them back into place. When you are ready to explore the mathematics that helps solve the puzzles, you will find what you need to know if in the book. Learn about conjugates and commutators and you will be ready to devise strategies for getting hte last few pieces into place, which is the hard part of the job. In addition to the Oval Track puzzles, the software package includes a version of the familiar "15" puzzle that you can modify in many ways, even to playing the puzzle on the surface of a cylinder or a torus. It also includes a computerized Hungarian Rings puzzle. There are programmable macro buttons that you can use to perform sequences of steps of any length, and the package gives you the capability of storing macro programs and inventing your own ways to configure the puzzles. The software is on the enclosed CD ROM in versions for both Windows and Macintosh operating systems. -- from back cover.
Contents: Software installation and a first tour -- An overview of oval tracks -- The transpose puzzle: An introductory tour -- The slide puzzle: An introductory tour -- The Hungarian rings puzzle: An introductory tour -- Permutation groups: Just enough definitions and notation -- Permutation groups: Just enough theory -- Cycles and trasnpositions -- The parity theorem -- The role of conjugates -- The role of commutators -- Mastering the oval track puzzle -- Transferring knowledge between puzzles -- What a difference a disk makes!: Changing the number of disks, and using Maple or GAP -- Mastering the slide puzzle -- Mastering the Hungarian rings with numbers -- Mastering the Hungarian rings with colors -- Advanced challenges.