12. Problem Corner
from Clear Thinking by R W Jepson

The five simple deductive problems that follow are added for those readers who like something in the way of a diversion from the more serious topics treated above. They are either taken from or founded upon the problems formerly set week by week by " Caliban " in the New Statesman.

1. Amy, Beryl, Cecily and Dorothy are married to Arthur, Basil, Cyril and David (not necessarily respectively), and each of the four husbands is brother to one of the ladies. Dorothy has no brothers. Amy's brother-in-law is married to Cecily. Beryl is married to Basil. Cecily's husband was at school with Arthur and David. Which of the ladies is Cyril's sister? (Give your argument in full.)

2. A train is controlled by an engine-driver, a fireman and a guard, whose names are Brown, Jones and Robinson, not necessarily respectively. On the train are three passengers: Mr Jones, Mr Robinson and Mr Brown. Mr Robinson lives at Leeds. The guard lives half-way between Leeds and London. Mr Jones's income is £400 2S. 1d. per annum. The guard earns in a year exactly one-third of the income of his nearest neighbour who is a passenger. The guard's namesake lives in London. Brown beat the fireman at billiards.
What is the name of the engine-driver? Give your argument in full.

3. To celebrate the sixth consecutive victory of the school in their annual rowing contest with Medford, the statue of Hercules which stood on the river bank in the public park was tarred and feathered. Suspicion pointed to one of the members of the school VIII. Whereupon Dr Evergreen called together the crew and the cox and asked each of them who was the culprit.

Adams: Jim Ebbels, Sir.
Belton: No, Sir, it was not Ebbels.
Chester: I did it, Sir.
Dodge: It was either Chester or Hammer, Sir.
Ebbels: Belton is not telling the truth, Sir.
Finch: It was Chester, Sir.
Graham: It was not Chester, Sir.
Hammer: It was neither Chester nor me, Sir.
Ison: Hammer is right, Sir; and it wasn't Ebbels either.

On the assumption that three, and three only, of these statements are true, who was the culprit?

"You know," I said to the Rector, "I find your sons very confusing. They are all at different colleges; they are all reading different subjects; each is keen on a different form of sport; and each contemplates a different vocation. It's hard to remember which to associate with what."
The Rector's eyes twinkled. "You should make it into a problem, Caliban."
"I would do," answered I, "if I had the data." Five days later I received the following post card

"Derek neither hunts nor shoots. The Selwyn man hates mathematics, the prospective barrister dislikes fishing. The hunting man has no interest in science. The Peterhouse man plays picquet with Bernard. The prospective clergyman is wishing he had read history. The climbing man detests languages, and the prospective barrister has no use for science. Derek is always poking fun at Peterhouse, the mathematician plays duets on the piano with Cohn. The languages man cannot ride, nor can the mathematician. Bernard is a year older than the Oriel man. Cohn is cleverer than the prospective journalist. The climbing man is younger than Derek. The prospective clergyman has never been to Cambridge. Neither of the Oxford men cares for climbing. Alaric keeps a dog at the Mitre. The fishing man buys his kit in Petty Cury. The prospective schoolmaster is the most popular of them all."

And the same afternoon I got the following telegram:

"Forgot to mention that the shooting man has no dog, and that one of the boys is at Christ Church."

Assign to each of the rector's sons his college, his subject of study, his favourite form of sport, and his intended career.
N.B.—Petty Cury is a street in Cambridge, not far from Selwyn and Peterhouse; the Mitre is a well-known hotel in Oxford.

The afternoon before a scholarship examination one of the Sixth Form boys of Wigby School entered the Headmaster's study and made a rough translation of a Greek prose paper that was lying on the table. The translation was found in the study which is occupied by Arfback, Bowler and Cribb; and it may be taken as certain that the culprit is one of these three boys. Haled before the Headmaster, they made the following statements:

Arfback: "I never entered your room all day, Sir."
Cribb: "Well, it wasn't either Bowler or me.
Bowler: "I -was feeling very unwell, Sir."
Cribb: "I can't do translation from the Greek, Sir."
Bowler: "That's quite true, Sir; he can't."
Arfback: "It certainly was not Bowler, Sir."
Bowler: "And I can vouch for Arfback's statement that he never came near the place."
Cribb: "Well, I was in Arfback's company all afternoon.
Arfback: "And it's quite true, Sir, that Bowler was far from well."

The Headmaster asked a Mr Dubb to investigate. The latter, an impertinent young man who was under notice, sent in the following report:

"DEAR HEADMASTER,—Nine statements were made to you by three suspects. Of these nine statements, three, and three only—one statement by each suspect—are true. I need say no more.—A. DUBB."

On the assumption that Mr Dubb's report is accurate, who translated the paper?

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