This preview shows page 1. Sign up to view the full content.
Unformatted text preview: aba1 b1 is a 3cycle. GK3. The “15 puzzle” is a puzzle with 15 sliding tiles in a 4 × 4 tray that you may have seen from time to time. In its solved position, the puzzle looks like this: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 The puzzle lets you switch the empty square with any tile that is next to it. The usual object of the puzzle is to put the puzzle in its solved position. Show that, starting from the solved position, it is not possible to switch the 14 and the 15, and leave all of the other tiles unchanged. (Hint: You should use odd and even permutations, but there is more to it than that.)...
View
Full
Document
This homework help was uploaded on 02/01/2008 for the course MATH 150A taught by Professor Kuperberg during the Spring '03 term at UC Davis.
 Spring '03
 Kuperberg
 Algebra

Click to edit the document details