h my envelope. "I forgot the
subaltern. Ah, that's right. The answer is a hundred and twenty-five
men.... No, that's wrong--I never doubled the half-crown. Er--oh, look
here, Herbert, I'm rather busy this morning. I'll send it to you."

"Right," said Herbert. "I know I can depend on you, because you're
mathematical." And he opened the door for me.

I had meant to do a very important piece of work that day, but I couldn't
get my mind off Herbert's wretched problem. Happening to see Carey at
teatime, I mentioned it to him.

"Ah," said Carey profoundly. "H'm. Have you tried it with an '_x_'?"

"Of course."

"Yes, it looks as though it wants a bit of an '_x_' somewhere. You
stick to it with an '_x_' and you ought to do it. Let '_x_' be the
subaltern--that's the way. I say, I didn't know you were interested in
problems."

"Well--"

"Because I've got rather a tricky chess problem here I can't do." He
produced his pocket chess-board. "White mates in four moves."

I looked at it carelessly. Black had only left himself with a Pawn and a
King, while White had a Queen and a couple of Knights about. Now, I know
very little about chess, but I do understand the theory of chess
problems.

"Have you tried letting the Queen be taken by Black's pawn, then
sacrificing the Knights, and finally mating him with the King alone?"

"Yes," said Carey.

Then I was baffled. If one can't solve a chess problem by starting off
with the most unlikely-looking thing on the board, one can't solve it at
all. However, I copied down the position and said I'd glance at it.... At
eleven that night I rose from my glance, decided that Herbert's problem
was the more immediately pressing, and took it to bed with me.

I was lunching with William next day, and I told him about the subaltern.
He dashed at it lightheartedly and made the answer seventeen.

"Seventeen what?" I said.

"Well, whatever we're talking about. I think you'll find it's seventeen
all right. But look here, my son, here's a golf problem for you. A is
playing B. At the fifth hole A falls off the tee into a pond--"

I forget how it went on.

When I got home to dinner, after a hard day with the subaltern, I found a
letter from Norah waiting for me.

"I hear from Mr. Carey," she wrote, "that you're keen on problems. Here's
one I have cut out of our local paper. Do have a shot at it. The answer
ought to be eight miles an hour."

Luckily, however, she forgot to enclose the proble