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## EXERCISE FOR PRISONERS.

(

The Guarded Chessboard)

The following is the plan of the north wing of a certain gaol, showing

the sixteen cells all communicating by open doorways. Fifteen prisoners

were numbered and arranged in the cells as shown. They were allowed to

change their cells as much as they liked, but if two prisoners were ever

in the same cell together there was a severe punishment promised them.

Now, in order to reduce their growing obesity, and to combine physical

exercise with mental recreation, the prisoners decided, on the

suggestion of one of their number who was interested in knight's tours,

to try to form themselves into a perfect knight's path without breaking

the prison regulations, and leaving the bottom right-hand corner cell

vacant, as originally. The joke of the matter is that the arrangement at

which they arrived was as follows:--

8 3 12 1

11 14 9 6

4 7 2 13

15 10 5

The warders failed to detect the important fact that the men could not

possibly get into this position without two of them having been at some

time in the same cell together. Make the attempt with counters on a

ruled diagram, and you will find that this is so. Otherwise the solution

is correct enough, each member being, as required, a knight's move from

the preceding number, and the original corner cell vacant.

The puzzle is to start with the men placed as in the illustration and

show how it might have been done in the fewest moves, while giving a

complete rest to as many prisoners as possible.

As there is never more than one vacant cell for a man to enter, it is

only necessary to write down the numbers of the men in the order in

which they move. It is clear that very few men can be left throughout in

their cells undisturbed, but I will leave the solver to discover just

how many, as this is a very essential part of the puzzle.

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