"What are you up to, Ward; noughts and crosses?"
"Square, you ass! look and see for yourself."
On closer examination I found that he had drawn a rough square and had subdivided it into nine smaller ones, by means of two horizontal and two vertical parallel lines, and the spaces thus formed he was busily filling in with the numbers 1 to 9.
"What happens when you finish it? Where does the magic part of the show come in?" I asked. "It seems a very tame sort of amusement."
"Not when you get thoroughly interested in it," replied Ward. "You see, the idea is to arrange the figures so that each of the horizontal, vertical, and diagonal rows make a total of fifteen. It takes a bit of juggling, I assure you, and I am told that even larger magic squares can be formed. Ah! That's done it."
With a slightly growing interest I watched Ward manipulate the figures until he arrived at the solution, which, for some unexplained reason, I copied down--
+---+---+---+ | 8 | 1 | 6 | +---+---+---+ | 3 | 5 | 7 | +---+---+---+ | 4 | 9 | 2 | +---+---+---+
"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.