The girl who shared Herbert’s meringue at dinner (a brittle one, which exploded just as he was getting into it) was kind and tactful.
“It doesn’t matter a bit,” she said, removing fragments of shell from her lap; and, to put him at his ease again, went on “Are you interested in little problems at all?”
Herbert, who would have been interested even in a photograph album just then, emerged from his apologies and swore that he was.
“We’re all worrying about one which Father saw in a paper. I do wish you could solve it for us. It goes like this.” And she proceeded to explain it. Herbert decided that the small piece of meringue still in her hair was not worth mentioning, and he listened to her with interest.
On the next morning I happened to drop in at Herbert’s office…. And that, in short, is how I was entangled in the business.
“Look here,” said Herbert, “you used to be mathematical; here’s something for you.”
“Let the dead past bury its dead,” I implored. “I am now quite respectable.”
“It goes like this,” he said, ignoring my appeal.
He then gave me the problem, which I hand on to you.
“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 teatime, I mentioned it to him.
“Ah,” said Carey profoundly. “H’m. Have you tried it with an ‘x‘?”
“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.”
“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 problem. For by this time, what with Herbert’s subaltern, Carey’s pawn, and a cistern left me by an uncle who was dining with us that night, I had more than enough to distract me.
And so the business has gone on. The news that I am preparing a collection of interesting and tricky problems for a new “Encyclopaedia” has got about among my friends. Everybody who writes to me tells me of a relation of his who has been shearing sheep or rowing against the stream or dealing himself four aces. People who come to tea borrow a box of wooden matches and beg me to remove one match and leave a perfect square. I am asked to do absurd things with pennies….
Meanwhile Herbert has forgotten both the problem and the girl. Three evenings later he shared his Hollandaise sauce with somebody in yellow (as luck would have it) and she changed the subject by wondering if he read Dickens. He is now going manfully through “Bleak House”–a chapter a night–and when he came to visit me to-day he asked me if I had ever heard of the man.
However, I was not angry with him, for I had just made it come to “three cows.” It is a cow short, but it is nearer than I have ever been before, and I think I shall leave it at that. Indeed, both the doctor and the nurse say that I had better leave it at that.