[Illustration]
+-----+-----+-----+-----+
| | | | |
| 8 | 5 | 10 | 11 |
|_____|_____|_____|_____|
| | | | |
| 16 | 13 | 2 | 3 |
|_____|_____|_____|_____|
| | | | |
| 1 | 12 | 7 | 14 |
|_____|_____|_____|_____|
| | | | |
| 9 | 4 | 15 | 6 |
| | | | |
+-----+-----+-----+-----+
In attempting to solve this puzzle it is clearly necessary to seek such
magic squares as seem the most favourable for our purpose, and then
carefully examine and try them for "fewest moves." Of course it at once
occurs to us that if we can adopt a square in which a certain number of
men need not leave their original cells, we may save moves on the one
hand, but we may obstruct our movements on the other. For example, a
magic square may be formed with the 6, 7, 13, and 16 unmoved; but in
such case it is obvious that a solution is impossible, since cells 14
and 15 can neither be left nor entered without breaking the condition of
no two men ever being in the same cell together.
The following solution in fourteen moves was found by Mr. G.
Wotherspoon: 8-17, 16-21, 6-16, 14-8, 5-18, 4-14, 3-24, 11-20, 10-19,
2-23, 13-22, 12-6, 1-5, 9-13. As this solution is in what I consider the
theoretical minimum number of moves, I am confident that it cannot be
improved upon, and on this point Mr. Wotherspoon is of the same opinion.