that the first knight's move can only be made by 1 or by 2 or by 10.
Supposing 1 moves, then the next move must be by 23, 4, 8, or 21. As
there is never more than one square vacant, the order in which the
counters move may be written out as follows: 1--21--14--18--22, etc. A
rough diagram should be made on a larger scale for practice, and
numbered counters or pieces of cardboard used.


343.--EXERCISE FOR PRISONERS.

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