Mathematical_Recreations-Kraitchik-2e

Games 297
first one to be unable to draw a line satisfying these conditions
is the loser.
19. PEG SOLITAIRE. The common property of the many
varied forms in which this game appears is that it is played
with a set of n objects and a board containing n + 1 receptacles
into each one of which just one of the objects may be
fitted. The objects, their number, the re~eptacles and the
arrangement of the receptacles may vary. We assume that
37 47 57
36 46 56
15 25 35 45 55 65 75
14 24 34 44 54 64 74
13 23 33 43 53 63 73
32 42 52
31 41 51
FIGURE 162. Peg Solitaire Board.
the objects are pegs, that the receptacles are holes in the
board, and that there are 37 holes arranged in the board as
in Figure 162. We shall use the numbering given in the
figure.
If some or all of the pegs are in position, a move is possible
only if there is a set of three consecutive holes in the same
horizontal or vertical of which two consecutive holes are occupied
and the third is vacant. When the move is possible
it consists in moving the peg at one end of the three holes to
the hole at the other end and removing the peg in the middle.
In other words, one takes as in checkers, but along horizontals
and verticals, not diagonals.
The game consists in starting with a given distribution of