THE TEN APPLES.
(
Moving Counter Problem)
The family represented in the illustration are amusing themselves with
this little puzzle, which is not very difficult but quite interesting.
They have, it will be seen, placed sixteen plates on the table in the
form of a square, and put an apple in each of ten plates. They want to
find a way of removing all the apples except one by jumping over one at
a time to the next vacant square, as in draughts; or, better, as in
solitaire, for you are not allowed to make any diagonal moves--only
moves parallel to the sides of the square. It is obvious that as the
apples stand no move can be made, but you are permitted to transfer any
single apple you like to a vacant plate before starting. Then the moves
must be all leaps, taking off the apples leaped over.
Answer:
Number the plates (1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14,
15, 16) in successive rows from the top to the bottom. Then transfer the
apple from 8 to 10 and play as follows, always removing the apple jumped
over: 9-11, 1-9, 13-5, 16-8, 4-12, 12-10, 3-1, 1-9, 9-11.
