Mathematical_Recreations-Kraitchik-2e

808 Mathematical Recreations
moves a number of the cycles are truncated because the
move that completes one cycle may cancel the move that
begins another.
FIGURE 168. The 15
Puzzle; One Permutation.
FIGURE 169.
We have selected the 15 puzzle as characteristic of permutational
games and puzzles. There are many, many variations.
In some of them variety is gained by a (real or
apparent) change in the shape of the path over which the
moves may be made, or in the number of cells involved. In
others the game may be competitive, with the first moves
made according to a pattern like one of those described.
2. Denote the columns of the ordinary chessboard by the
letters from a through h and the rows, starting from White's
side, by the numbers from 1 through 8.
Place seven white pawns on cells aI, bl,· .., gl, and seven
black pawns on cells h2, ..., h8. Each pawn may move to a
neighboring empty cell in this row and column, and each
pawn may leap over (without taking) a pawn of the opposite
color in an adjacent cell, provided the following cell is empty.
Also, one diagonal move is permitted - that between gl
and h2 in either direction. The object of the game is to get