Part 3

‘Ah, well,’ said the chairman, ‘I must turn to Mr Pusely-Smythe, who is acting as secretary for us to-night. I presume he has added one more to his list of triumphs.’

‘The pangs of failure,’ said that saturnine gentleman, ‘are increased by the jeers of the learned chairman. I ought to have won. I claim to have won. But I confess that it will not surprise me if I am reduced to an equality with my artist friend. I shall have a melancholy pleasure in sharing the prize with him. He tried to work upon gratitude, and so did I. The particular brand of gratitude that I decided to exploit for my purpose was the gratitude that a woman feels for the return of her lost pet dog. It seems to vary inversely as the value of the dog, but it is always great.

‘You will perhaps remember that about a year ago Leonard set us a peculiarly sinful problem, which he styled the Substitution Problem, and that in the complicated and unjustifiable operations by which I succeeded in winning the prize I made the acquaintance of James Tigg, and did him a good turn. Now James, known to his intimate friends as “Kidney,” is by profession a French polisher, but does not practice, and his favourite occupation is the appropriation of dogs, his gifts in that direction amounting almost to genius.

‘I sent for James. I told him that I thought it likely that three ladies, living in different suburbs, would lose their pet dogs and that I should know where to find them, and should be enabled by the address on the dog-collar to return each of the little darlings to its owner. At the same time I put five golden sovereigns on the table.

‘“Likely?” said James. “It’s a ruddy certainty.” He then picked up the coins in an absent-minded way and instructed me as to details.

‘Two days later, at an early hour in the morning, I called on Lady Pingle at her house at Epsom with her ladyship’s alleged Pekingese under my arm. I told her how I had found the poor little thing wandering on Wimbledon Common late the night before almost in a state of collapse, had given it food and shelter, and had taken the earliest opportunity to relieve her anxiety by its return.

‘Her gratitude was almost frantic. She kissed the dog ardently, and at one moment I was almost afraid she was going to kiss me too. She did not do that, but she did insist on my breakfasting with her, and I accepted. And let me tell that over-educated sybarite Matthews, with his sneers at casual hospitality, that he himself never breakfasted better.

‘I lunched with Mrs Hastonbury at her residence at Leatherhead. In this way she showed her gratitude for the return of “Bimby”—a chocolate-coloured Pom with a short temper. But I must confess that she was not nearly as quick off the mark as Lady Pingle. I had to inquire about hotels in the neighbourhood before she saw which way her duty lay.

‘The third dog that I had to deliver, a mouldy little pug, belonged to the wife of a curate living much nearer home. She was grateful and she was hospitable. She said that they never dined but that they were just sitting down to high tea, and she hoped I would join them. It was an evening meal substituted for dinner, and I contend that I am entitled to count it as dinner.’

‘Kindly tell us what you had,’ said the chairman.

‘What? The internal evidence? Certainly. I had cocoa, scrambled eggs, and seed-cake. And I hope you will take a lenient view of it.’

‘Your hostess herself maintained that it was not dinner, and the internal evidence, as you call it, entirely supports her view. Your career of crime will only give you a score of two. The high tea is disallowed. I will now call upon Major Byles.’

‘The sacrifice that I made to luck on the occasion of our last competition,’ said Major Byles, ‘has brought me success at last. I claim to be a winner, and await your decision with confidence. It happened that two of my friends both wanted a furnished house at Brightgate for the winter, and did not want the bother of going down to make their selection. I saw my chance at once. I might never have thought of it, but I didn’t miss it when it was shoved at me. I said at once that I was thinking of running down to Brightgate for a day or two, and that it always interested me to look over houses. They told me their requirements and let me take on the job for them.

‘The house-agent at Brightgate had only six houses on his books that were at all suitable. He gave me orders to view, and I started business at eight one morning. I started badly.

‘At the first house a proud but pretty parlour-maid told me that it was not usual to show furnished houses at that hour, but I could call again at eleven. At the second house there was only a caretaker. That left me with, so to speak, four cartridges and three birds to kill. I hurried on to the third house, which was half a mile away. By a bit of luck I met the owner on the doorstep, and told him my alleged business.

‘“You’re very early,” he said. “Why, we haven’t had breakfast yet.”

‘“No more have I,” I said. “But last year I lost a good house through being too late, and I thought I wouldn’t make the same mistake again.”

‘He was a genial old chap. He said the best thing I could do was to come in and breakfast with him, and by the time I had finished the servants would have got the bedrooms tidied up. I did my best to accept with decent hesitation.

‘At lunch-time I tried the fourth house on my list and struck another caretaker. I couldn’t afford another miss. I got lunch at the fifth house, but I had to be no end complimentary before I could get them up to the point. In fact, it wasn’t till I told the woman that her pimply-faced son was a fine upstanding young fellow that she decided to order the extra chop.

‘But at the sixth house I had no trouble about dinner. The owner turned out to be a friend of a friend of mine. He fetched up a bottle of the ’87 in my honour and insisted on my stopping the night.

‘They were all _pukka_ meals, and all the conditions were observed. Am I a winner, Mr Chairman?’

‘Certainly. Does anybody else claim to be a winner?’

‘I do,’ said Dr Alden. ‘The day before yesterday a doctor rang me up and asked me to see a patient of his—a woman with a wealthy, devoted, and very nervous husband. That was at eight in the morning. My car happened to be at the door, and it suited me to go right away. I saw the patient, was able to reassure the husband, and had breakfast with him. Later in the morning a man was introduced to me who was interested in old glass and had heard of me as a collector. He was very keen that I should lunch with him and see what he had got. He was a pleasant chap and I accepted. When I got back, a doctor, quite an old pal of mine, said that he was going to take me to dine that night with a man I had never seen before. It seemed that the stranger had staying with him for one night a French specialist in my own line. The Frenchman was anxious to meet me, and his host was anxious to please him. So he had tried to arrange it through a mutual friend. I was myself keen to meet that Frenchman, and so he succeeded.

‘Of course, I didn’t arrange all this—couldn’t have arranged it. As a matter of fact, I had never intended to compete this time. But destiny decided to take a hand in this competition. I claim to be a winner.’

‘An interesting point,’ said the chairman. ‘Can a man be said to win who has never competed? I shall decide in Dr Alden’s favour. Leonard says nothing of intention. He only demands certain facts. And these facts the doctor by an amazing stroke of luck has been able to provide. The prize of one hundred and ten pounds will be divided equally between him and Major Byles, unless there is any further claim.’

No further claim was forthcoming. The chairman then announced that Mr Matthews would preside at the next meeting, and read out the problem set for the following month, called ‘The Win-and-Lose Problem,’ and there was a general feeling that it would take some doing.

No. IV.

The Win-and-Lose Problem

At the forty-sixth meeting of the Problem Club, the waiters having left the room, Mr Matthews, smiling and rubicund, took his place as chairman. He finished his glass of an old and veritable cognac, lit with care and a cedar-wood spill a cigar that can only be obtained by the favour of the planter, and read out the terms of the Win-and-Lose Problem.

‘It is required to win an even bet of one pound, resulting in a net loss of one pound to the winner; and to lose an even bet of one pound resulting in a net gain of one pound to the loser. No competitor is to make more than two bets.’

‘Well, gentlemen,’ said Mr Matthews, ‘I’m supposed to make one or two preliminary observations. Now here’s a thing that strikes me. You may remember that when we tackled the Kiss Problem, our reverend friend Mr Cunliffe said that it revealed the artful Leonard as an apostle of morality. Of course, the padre took the jack-pot on that occasion, and so he may have been prejudiced, but it looks to me now as if he may have been right. See for yourselves. You’ve got to win a bet and lose money by it, and then you’ve got to lose a bet and make money by it, and at the end of it you’re left just where you were when you started. There’s not much deadly fascination and excitement about that—why, it’s enough to make you lose your taste for gambling.

‘Yes, and there’s one more point. I noticed a good deal of preoccupation at dinner to-night. Very few of you seemed to be putting your heart into the work, and I believe I was the only man who had the _vol-au-vent_ brought back to him for further reference. Great mistake that of yours. Some of you tried to work out sums on the back of your menus. I detected Major Byles, with corrugated brows, in the act of making pencil calculations on the tablecloth. Yes, there’s not a doubt that Leonard has given you a worrying time, and some of you were wrestling with it right up to the last moment. It won’t surprise me if there’s not a winner among the whole lot of you. However, we’ll begin with a likely chance. You, Sir Charles, have got a reputation as a learned man; can I ask the secretary to draw a cheque in your favour?’

‘I’d be sorry to stop you,’ said Sir Charles, ‘but I’m afraid I can’t claim it. Archæology don’t help with arithmetic. As an eminent classical scholar once observed, I’ve not got the low cunning that makes a mathematician. The only thing I could think of was to insure the chances of each bet appropriately, but it seemed to me that you would regard such insurance as being in itself a bet.’

‘I certainly should. You don’t change a thing by changing its name. You are limited to the two bets, and I shall not allow four even if you call two of them insurance. Come now, Jimmy, have you profited sufficiently by your racing experiences to have won the prize to-night?’

‘Profited by my racing experiences?’ said the Hon. James Feldane wearily. ‘If you’d go and talk to the bank that has charge of my overdraft you wouldn’t use words like those. But backing horses, though it’s a mug’s game, is, at any rate, easy. There are too many complications in Leonard’s fancy work for a simple child of Nature like myself. I can’t engineer a two-cylinder gamble with a double back-jump actuated by the cam-shaft. The only man I know who could face it without mental overstrain is my bookmaker. He’s a wonder. He’d give you fifteen different ways of perforating this problem inside a minute. No juggle with figures can beat him. I don’t know if you’d call it a talent or a disease, but I’ve not got it. As a competitor, I’ve failed, but I don’t mind admitting that I’ve made a little actual money out of the competition.’ Jimmy smiled reminiscently.

‘May we have the details?’ asked the chairman.

‘I’d sooner you got them from Hesseltine.’

The chairman called upon Mr Hesseltine.

‘I don’t wonder,’ said that young man, ‘that Jimmy don’t like to tell you. If I’d stolen money from a crossing-sweeper in St James’s Street I shouldn’t be proud of it myself. The silly ass thinks he’s scored off me, but as I was out to lose a quid anyhow——’

‘May we have the actual facts?’ suggested the chairman.

‘Certainly. I was thinking about this problem and I got a sudden brain-wave. I saw how to do the first half—to win a bet of a pound that would leave me one pound down when I’d won it. Well, I happened to be going up St James’s Street with Jimmy later that morning, and by way of leading up to it I asked him what he generally gave to a street-beggar. “Nix,” he said. “What do you?” So I told him that I generally gave a sovereign. He told me in his coarse sort of way that he didn’t believe it. That was what I had expected. “All right,” I said, “I’ll bet you a pound that I give two golden sovereigns to the next beggar or crossing-sweeper I come across.” He thought about it and then said: “I’ll take that, and to guard against accidents I’ll be the next beggar. Give me a little assistance, kind sir?”

‘Of course, in that way he put himself on velvet. Whether I decided to win my bet or to lose it, Jimmy had to make one sovereign out of me. Didn’t affect me at all, for according to Leonard I’d got to win my bet and lose a pound by it, which I did. The only person hit was the crossing-sweeper up the street, who would otherwise have made two quid. Of course, what I ought to have done was to have handed Jimmy over to the police for begging—wish I’d thought of it.

‘Well, I negotiated the first half of the problem, but the second half beat me. I’m inclined to think the sting of the beast is in its tail. It takes two people to make a bet. I’m not a poet or any sort of imaginative chap, but I could think of a bet which for a dead certainty it would pay me to lose. I couldn’t think of anybody, even including that rotter Jimmy, who would be fool enough to take it. You must try somebody else, Mr Chairman.’

‘Major Byles?’ the chairman suggested.

‘As a head-waiter,’ said the Major, ‘I’ve got nothing against Leonard. As a setter of problems he’s given general satisfaction, but this time I should like to back my bill to the effect that he has mixed up too much arithmetic with the sport. I’ve spent a month on this win-and-lose business, all the time with the feeling that a boy fresh from school would work out the whole thing on the back of an envelope in ten minutes, and I’ve done nothing. I spent the first fortnight at home, and at the end of it I had contracted insomnia, headache, and what you might call pardonable irritability. At the end of that time my wife said that of course she had noticed the change, and that I seemed to be doing sums all day, and that if we were ruined I had better say so and she would face it bravely. I reassured her and came to town on important business. I used tons of the club notepaper for my calculations, put an undue strain on the club wastepaper-baskets, quarrelled with two of my best friends, was sarcastic in addressing club servants, and am expecting a letter from the committee to ask for my resignation. The amazing thing is that all the time I have been on the very point of getting the solution. In my opinion it’s the most horribly worrying thing that Leonard has ever given us.’

‘Well,’ said the chairman, ‘artists are not generally supposed to be particularly strong at arithmetic, but I’ll ask Mr Wildersley what he’s done about it.’

‘Can’t say I agree with the Major,’ said Wildersley. ‘I call it a jolly easy problem, and I claim to be a winner. It didn’t take me any time to think of it, either. I got a man into my studio, to see alleged works of art, and I said to him that I would bet him a pound I would give him two pounds. He took me. “You’ve lost,” I said. “Pay up, and then I’ll pay up.” He handed me a sovereign and I handed him two pounds of potatoes in a paper bag. So I’d won a pound in money and lost two pounds in potatoes. If you win one pound and lose two, that makes a net loss of one pound on the transaction, and so I’d done the first half of the problem.

‘The chap seemed to be grumbling rather. “What’s the matter with you?” I said. “The green-grocer told me that they were the kind he eats himself, and that he could guarantee them.”

‘“I don’t want the beastly potatoes,” he said. “The whole thing’s a dirty swindle.” I thought he’d say that. So I told him that it was no swindle and I would be quite willing to take the same bet myself. He jumped at it, but to make sure he said he would bet me a sovereign he would give me two pounds. I took him, lost, paid the sovereign, and got back my two pounds of potatoes. That finished the second half of the problem. I’d lost a bet of one pound, and had made two pounds, giving a net gain of one pound. Naturally he wanted to know what I had done it for, and I said it was to stop him from trying to talk about art—the chap’s a critic.’

Mr Matthews took two minutes and a brandy-and-soda before giving his decision as follows:—

‘Ingenious, but it won’t do. Mr Wildersley professes to have subtracted money to the value of a sovereign from two pounds by weight of potatoes, and to have got a result of one pound. Of what did that pound consist? Even after dinner we can’t have mental confusion of this kind. The claim is disallowed.’

Mr Harding Pope, M.P., made an uninteresting confession of failure, and the chairman then called upon Mr Quillian, K.C., who was acting as secretary for the evening.

Mr Quillian removed his pince-nez and glanced round the room with that look of amiable superiority that some people found irritating.

‘I claim to have won this fairly simple competition,’ he said. ‘Of course, it has a psychological as well as an arithmetical side; the bets have to be actually made and not merely worked out on paper. I made my plan one afternoon, and then went over to my club to see if I could find my friend Blenkinsop. He is generally at the club at that hour, and I felt sure that he would accept the two bets that I had to propose.

‘Well, as it happened, Blenkinsop was not at the club, but I found Mr Pusely-Smythe alone in the smaller reading-room. I’ve had to submit to a good deal of chaff—not particularly amusing—from Pusely-Smythe, and by way of return it seemed appropriate that he should help me to win our one hundred and ten pound prize. Also, if he will forgive me for saying so, he has just the commonplace shrewdness that I required in my victim.

‘After a little preliminary conversation, I produced my sovereign-case. I told him that there was a certain sum of money in gold in that case, and that I was willing to bet him a sovereign I would make him a present of it. He said, as I knew he would, that this meant that the sum of money in the case was half a sovereign, and that in consequence he would lose ten shillings on the transaction if he took the bet.

‘“Yes,” I said, “there is that possibility, but I am willing to protect you against it by a second bet. We will agree that the loser by the first transaction shall have the option to give the other man double what he has lost for double the sum now in my sovereign-case. And I will bet you a sovereign that he will not exercise that option. You see how it works out. If the sum in my sovereign-case is half a sovereign, as you suppose, you will lose ten shillings on the first transaction, but you will win a sovereign on the second transaction by exercising an option to exchange twenty shillings for twenty shillings.”

‘Without taking the time to think, he accepted both bets. I then opened my sovereign-case and showed him that it contained two pounds. I gave them to him, and as by so doing I had won my bet he gave me one of them back again. Kindly observe that I had now solved the first part of Leonard’s problem. I had won an even bet of one pound the net result of which was that I had lost a pound. Having made myself the loser on the first transaction, I now had the option to exchange twice my loss against twice the sum that had been in the sovereign-case—that is, to exchange two pounds for four pounds. I had bet that the loser would not exercise this option. I lost the bet and exercised the option. Thus, I lost an even bet of one pound with the net result that I made one pound. This settles the second half of the problem. I await, sir, with confidence, your decision in my favour.’

Mr Matthews referred once more to the terms of the problem. ‘Yes,’ he said, ‘it seems to me that you have met all Leonard’s requirements. Very smart bit of work, in my opinion. You take the club cheque for one hundred and ten pounds, unless, of course, some claim to share it with you is substantiated. Is there any such claim?’

‘Naturally, there’s mine,’ said Pusely-Smythe, with his deceptive air of melancholy.

‘Yours? How did you do it?’