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The Principle of Parity in Analyzing Puzzles

Matt Coppenbarger, Math Dept. University of Rochester

Thursday, March 16, 7PM Hylan 202

URL: http://home.rochester.rr.com/mcoppen1/puzzle.html

ABSTRACT:

The mathematical principle of parity is the simple and obvious fact that an even number is not equal to an odd number. It is a powerful tool that is usually restricted for use in impossibility proofs, but it can also be used as a way to make some very challenging puzzles where the solutions utilize the principle of parity. This talk will cover many puzzles, starting with the well-known 15 Puzzle, the impossibility of the 14-15 Puzzle, and three other sliding block puzzles.

In addition, five construction puzzles using various polyform pieces will be introduced, including a more elaborate version of the Soma Cube. Lastly, a brief discussion of the as yet unsolved Eternity Puzzle. This last puzzle originated in the Britain and still offers a $1.4 million prize to the first person to send them a complete solution. Solutions of most puzzles will not be provided, but clues on how to find the solution will be given. A number of the discussed puzzles will be available afterwards. No special knowledge of mathematics is needed to understand the material presented.