Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them

By John O. Kiltinen

Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to the theory of permutation groups. They are relatively simple to describe in group theoretic... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0883857251
• ISBN13: 9780883857250
• Release Date: October 2003
• Publisher: Mathematical Association of America (MAA)
• Length: 322 Pages
• Weight: 1.34 lbs.

Customer Reviews

Permutation puzzle challenges that never end

This package of book and software presents three fundamental puzzles that can be solved using permutations. The first is called the "Oval Tracks" puzzles and consists of an oval-shaped track that contains numbered disks. There are two fundamental operations that can be performed on the disks: *) All can be rotated around the track a certain number of positions in either direction. This movement will maintain the fundamental order of the disks. *) A certain set of permutations can be performed on a small number of the disks. The second category of puzzle is the "slide puzzles." In this case there is a rectangular grid where each cell of the grid contains a single disk. There is an empty cell and the disks are moved one at a time into the unoccupied cell, creating a different unoccupied cell. Variations of this puzzle have cells marked with an X that are rigid and cannot be moved. The third category of puzzles is called the "Hungarian Rings." In this case, the puzzle is constructed from two interlocking rings of disks that are either numbered or colored. The disks share two locations and are separately movable so the only operations are rotating the disks. In all cases, the player is given start and final configurations and the goal is to move from the start to the final state. The software can be used to execute a random rearrangement of the disks at the start of the game. Undo buttons and the ability to create complex macro operations are available. Using the fundamentals of group theory as it is applied to permutation groups, you can solve all of these games. Therefore, after the initial descriptions of the games, there is an introduction to group theory and permutations. The fundamental notation and operations are given, which is a lead in to the construction of more complex macros of the combination of permutations. While the exposition is quite clear, it will be difficult for anyone lacking knowledge of group theory to understand some of the abstract operations. Given that software is used and the large number of possible permutations of the disks, it is not possible for anyone to work through all of the challenges these games can present. Like the best puzzles, you can spend hours working through them, even with the help of the group theory. Hence the fun, as there is always another challenge to be faced and overcome.