THE TEN PRISONERS.
(
Moving Counter Problem)
If prisons had no other use, they might still be preserved for the
special benefit of puzzle-makers. They appear to be an inexhaustible
mine of perplexing ideas. Here is a little poser that will perhaps
interest the reader for a short period. We have in the illustration a
prison of sixteen cells. The locations of the ten prisoners will be
seen. The jailer has queer superstitions about odd and even numbers, and
he wants to rearrange the ten prisoners so that there shall be as many
even rows of men, vertically, horizontally, and diagonally, as
possible. At present it will be seen, as indicated by the arrows, that
there are only twelve such rows of 2 and 4. I will state at once that
the greatest number of such rows that is possible is sixteen. But the
jailer only allows four men to be removed to other cells, and informs me
that, as the man who is seated in the bottom right-hand corner is
infirm, he must not be moved. Now, how are we to get those sixteen rows
of even numbers under such conditions?
Answer:
It will be seen in the illustration how the prisoners may be arranged so
as to produce as many as sixteen even rows. There are 4 such vertical
rows, 4 horizontal rows, 5 diagonal rows in one direction, and 3
diagonal rows in the other direction. The arrows here show the movements
of the four prisoners, and it will be seen that the infirm man in the
bottom corner has not been moved.
