[Illustration: A magic square.]
"There are other arrangements of the numbers," he remarked; "for instance, you can get another magic square by exchanging the top and bottom lines or the outside vertical columns; but I have not managed a larger square yet. Hello! Here comes Newman, so it must be close on half-past five."
The miserable hour over, I made my way homewards, revolving in my mind the problem of Humphrey Trevena's cipher, till by some unaccountable impulse, as I was sitting in the ferry-boat that plies between Fowey and Polruan, I formed some hazy connection between Ward's magic square and the exaggerated chessboard design that was so sorely puzzling my father and uncle.
Rapidly the connection grew, till by the time the boat ran alongside Polruan quay-steps I firmly assured myself that Old Humphrey's cipher was based on the principle of a magic square; and, arguing that the solution of the "fifteen" square must be governed by some fixed rule, I determined to try to solve the working of Ward's puzzle, and to apply the principle, if possible, to the more complicated cipher.
With this object in view, I began my task. My father and uncle had gone out to the Yacht Club, so that I knew I should be free from interruption.
My first step was to make a copy of the magic square and indicate the order of the numbers by straight lines from one to the other. When completed, the diagram looked positively bewildering, and the only information I could gather was that the numbers 4, 5, 6 formed one of the diagonals, and ran obliquely from the bottom left-hand corner to the upper right-hand one, and that the centre number was the 5, or, the numeral next to half the highest number of the squares.
Next I tried a "twenty-five" square, the diagonal reading 11, 12, 13, 14, 15. The position of the 1 I had already fixed by that in the smaller square, which, by a sudden inspiration, I remembered occupied the same relative position in Humphrey Trevena's cipher. As in the "nine" square the 7 came immediately below the 6; I adapted the principle by placing the 16 in the square below the 15.
All this took time, but I felt satisfied that I was on the right track, till I came to the rest of the numbers, and, try how I would, I could not apply the principle any farther.