I pointed out that it was impossible to get all the letters into the box
under the conditions, but the puzzle was to place as many as possible.
This requires a little judgment and careful investigation, or we are
liable to jump to the hasty conclusion that the proper way to solve the
puzzle must be first to place all six of one letter, then all six of
another letter, and so on. As there is only one scheme (with its
reversals) for placing six similar letters so that no two shall be in a
line in any direction, the reader will find that after he has placed
four different kinds of letters, six times each, every place is occupied
except those twelve that form the two long diagonals. He is, therefore,
unable to place more than two each of his last two letters, and there
are eight blanks left. I give such an arrangement in Diagram 1.
[Illustration: 1]
[Illustration: 2]
The secret, however, consists in not trying thus to place all six of
each letter. It will be found that if we content ourselves with placing
only five of each letter, this number (thirty in all) may be got into
the box, and there will be only six blanks. But the correct solution is
to place six of each of two letters and five of each of the remaining
four. An examination of Diagram 2 will show that there are six each of C
and D, and five each of A, B, E, and F. There are, therefore, only four
blanks left, and no letter is in line with a similar letter in any
direction.