THE SIBERIAN DUNGEONS.
(
Magic Squares Problem.)
The above is a trustworthy plan of a certain Russian prison in Siberia.
All the cells are numbered, and the prisoners are numbered the same as
the cells they occupy. The prison diet is so fattening that these
political prisoners are in perpetual fear lest, should their pardon
arrive, they might not be able to squeeze themselves through the narrow
doorways and get out. And of course it would be an unreasonable thing to
ask any government to pull down the walls of a prison just to liberate
the prisoners, however innocent they might be. Therefore these men take
all the healthy exercise they can in order to retard their increasing
obesity, and one of their recreations will serve to furnish us with the
following puzzle.
Show, in the fewest possible moves, how the sixteen men may form
themselves into a magic square, so that the numbers on their backs shall
add up the same in each of the four columns, four rows, and two
diagonals without two prisoners having been at any time in the same cell
together. I had better say, for the information of those who have not
yet been made acquainted with these places, that it is a peculiarity of
prisons that you are not allowed to go outside their walls. Any prisoner
may go any distance that is possible in a single move.
Answer:
+-----+-----+-----+-----+
| | | | |
| 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.
