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.
[Illustration]
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.