Make a diagram of
any convenient size
to that shown in our illustration, and provide six
to represent foxes and three to
Place the geese on the
discs 1, 2, and 3, and the foxes on the discs numbered 10, 11, and 12
Now the puzzle is
By moving one at a time,
fox and goose
alternately, along a straight line from one disc to the next one, try
get the foxes on 1, 2, and 3, and the geese on 10, 11, and
make them exchange places—in the fewest possible moves.
But you must be
careful never to let a fox and
within reach of
each other, or there will be trouble.
This rule, you will find,
you moving the fox from 11 on the first move, as on either 4 or 6 he
would be within reach of a goose.
It also prevents your moving a fox
10 to 9, or from 12 to 7. If you play 10 to 5, then your next move may
2 to 9 with a goose, which you could not have played if the fox had not
previously gone from 10.
It is perhaps unnecessary to say that only one
fox or one goose can be on a disc at the same time.
Now, what is the
smallest number of moves necessary to make the foxes and geese change