"A subaltern riding at the rear of a column of soldiers trotted up to the captain in front and challenged him to a game of billiards for half-a-crown a side, the loser to pay for the table. Having lost, he played another hundred, double or quits, and then rode back, the column by this time having travelled twice its own length, and a distance equal to the distance it would have travelled if it had been going in the other direction. What was the captain's name?" Perhaps I have not got it quite right, for I have had an eventful week since then; or perhaps Herbert didn't get it quite right; or perhaps the girl with the meringue in her hair didn't get it quite right; but anyhow, that was the idea of it. "And the answer," said Herbert, "ought to be 'four cows,' but I keep on making it 'eight and tuppence.' Just have a shot at it, there's a good fellow. I promised the girl, you know." I sat down, worked it out hastily on the back of an envelope, and made it a yard and a half. "No," said Herbert; "I know it's 'four cows,' but I can't get it." "Sorry," I said, "how stupid of me; I left out the table-money." I did it hastily again and made it three minutes twenty-five seconds. "It _is_ difficult, isn't it?" said Herbert. "I thought, as you used to be mathematical and as I'd promised the girl----" "Wait a moment," I said, still busy with 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 tea-time, 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 seen to it that he 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.