## 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.