Edward Winter's Chess Explorations (48)

‘Below is the “score” of a game found in A.D. Brunswick’s rooms after his death under mysterious circumstances. It was in Brunswick’s handwriting. At first it aroused no suspicions, but Inspector Snooper, a keen chessplayer, saw at once that it was some sort of cryptogram.’

‘What was Brunswick’s message?’

‘The competitors in the Rookwood Chess Congress are organized in two sections. In each section each competitor plays one game against each of the other competitors in that section.

This meant, last year, that the secretary had to arrange 165 games. This year there is one more competitor in each section.

How many games must the secretary arrange?’

‘“For the purposes of our chess tournament”, said Woodpusher, “we divided our players into two groups. Each player played two games against each other player in his group. That did away with all possibility of unfairness in regard to the opening move.”

“There must have been a large number of games played altogether.”

“Exactly 200”, said Woodpusher.

How many players in all took part in the tournament?’

‘Representatives of Doomshire and Gloomshire met to play chess over 100 boards. Both men and women players took part; each county producing more than 50 men players.

More women played for Gloomshire than for Doomshire.

It was arranged that, so far as possible, men should be matched against men and women against women. This meant that there were only mixed matches (men versus women) to the extent to which the number of men players representing Doomshire exceeded the number of men representing Gloomshire.

On the boards where men were matched against men, Doomshire won three matches out of five. On the boards where women were matched against women, Gloomshire won two matches out of three. And on the boards where Doomshire’s surplus men met Gloomshire’s surplus women, the Doomshire players won two-thirds of the matches. No game ended in a draw. The result was a very narrow win for Doomshire by 51 games to 49.

How many men played for Doomshire?’

‘“I’m competing”, said Gambitt, “in the Minor Open Reserves at Prawnville.”

“Oh yes? Do you expect to win a prize?”

“Can’t say. There are four prizes altogether.”

“And how many competitors?”

“Twelve. But of course they may divide one or more of the prizes. Scoring is on the usual plan, you see: one point for a win, half a point for a draw. One year all 12 competitors scored five and a half points; the four prizes were divided among them. Last year three competitors tied for first place – they shared the first three prizes – then came three more competitors with equal points; they divided the fourth place. So, you see, there’s always a chance.”

“If I were you, Gambitt”, I said, “I wouldn’t be too ambitious. Aim at scoring just enough points to be certain of at least a share in a prize.”

“Good idea”, said Gambitt, “but how many points is that?”

How many points is it?’

‘When Mrs Orme went into the nursery the children were playing with the chessmen.

“What are you doing, dears?”

“Why”, said Ronnie, “Clara and I were talking about our phone number. Clara says it has 32 pairs of factors.”

“So it has”, said Mrs Orme, who had worked that out herself. “But why the chessmen?”

“There are 32 of those”, said Ronnie. “I was putting one back in the box as I worked each pair of factors out. But, Mummy, there’s something wrong. I’ve finished my calculations, and there are still these eight black pawns.”

Mrs Orme took a hasty glance at his notebook. “Ronnie”, she said, “you are a duffer. You’ve got the number wrong.”

“Got the number wrong?” echoed Ronnie.

“Of course. You wouldn’t call yourself Rome, now would you?”

What is the Ormes’s phone number?’

‘During the recent rebellion in Jehannum, a native runner was brought into the small fortified station of Ustaraf, which was occupied by a detachment of the Wellshires, and was found to be carrying in the folds of his pagri a tightly-folded paper, which he gave up without demur. The only writing on it was the following:

Major ffeatherstonehaugh-Haugh, a keen but incompetent chessplayer, who was in command, was greatly interested, and guessed that it must be a chess problem sent to him by Legge-Pullar, who had taught him the rudiments of the game, and whom he knew to be on Intelligence duty somewhere in the interior. He therefore set himself to solve the problem, which seemed to be rather unusual; so unusual, in fact, that three days later he had made nothing of it when another runner was brought in, bearing a paper on which the following was written:

AHAMIT TOT THAR TINALI EFAI ETCHL KRPS SOTTURA EPASTAI APONRR NIWDSIN IHLGT.

Major ffeatherstonehaugh-Haugh regrets he is unable to make head or tail of this, and begs you to translate it for him, as he is not familiar with any Oriental language.’

‘When I met Professor Graeme Atta the other day he showed me an interesting old manuscript book which he had come across when he was browsing among the second-hand bookstalls in Charing Cross Road. The book plate was almost indecipherable, but as far as I could make out bore the inscription “ex libris Samueli Loyd”. One of the pages contained a curious Latin cryptogram which seems to be of more than passing interest. Here is a copy of it:

Quot annos nata est Maria?’

‘This clever young carpenter received a chest of tools for a Christmas present, and immediately set to work to make a fine chessboard to present to Dr Lasker, the chess champion of the world. Dr Lasker is a great mathematician and puzzlist as well as a marvelous chessplayer, but can he beat our puzzlists in discovering the largest number of different pieces that the carpenter could have used in making this board?

Each piece must be made up of squares. One piece can be a single black square, another piece a single white square. Only one piece may consist of two squares, because all two-square pieces are alike. But a three-square piece has four different forms – a straight row with a black square in the middle, a straight row with a white square in the middle, a crooked piece with one black square, and a crooked piece with one white square. When you have divided the checkerboard into the greatest number of pieces, you will have solved the puzzle.’

‘I have a single chessboard and a single set of chessmen. In how many different ways may the men be correctly set up for the beginning of a game? I find that most people slip at a particular point in making the calculation.’