342 Answerscase the warders have the opposition, and can win. We will give a specimen
game. The warders' moves are above the line, the prisoners' below:
19-2022-14 20-21 14-13 21-2213-12 22-23 12-20 23-3120-19
17-1824-23' 18-26 23-31 '26-27 31-32' 27-26 32-40' 40-3226-34'
31-32 Capture, 19-27 27-26 26-25 Capture.
34-33 33-25'There is no possible escape for the prisoners if each warder pursues his
proper man.- GRASSHOPPERS' QUADRILLE
If we regard only the central column containing three white and three black
pieces, these can be made to change places in fifteen moves. Number the seven
squares downwards I to 7. Now play 3 to 4,5 to 3, 6 to 5, 4 to 6, 2 to 4, I to
2,3 to 1,5 to 3, 7 to 5, 6 to 7, 4 to 6, 2 to 4,3 to 2,5 to 3, 4 to 5. Six of these
moves are simple moves, and nine are leaps.
There are seven horizontal rows of three white and three black pieces, if we
exclude that central column. Each of these rows may be similarly interchanged
in fifteen moves, and because there is some opportunity of doing this in
every case while we are manipulating the column-that is to say, there is
always, at some time or other, a vacant space in the center of every row-it
should be obvious that all the pieces may be interchanged in 8 X 15 = 120
moves.- THE FOUR PENNIES
First place the four pennies together as in the first diagram; then remove
number I to the new position shown in the second diagram; and finally,