"What are you up to, Ward; noughts and crosses?"

"Noughts and crosses, my grandmother!"

"What, then?"

"Trying my hand at a magic square."

"A magic what?"

"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—