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“This One” is Disentangled!

The trouble began when a travelling New Zealand businessman was marooned at the Station Hotel in Leeds one wet night. Being a businessman he didn't read books or enjoy the gramophone or talk sport, so in despair his Leeds acquaintance turned to puzzles and tricks. After several problems based upon expert use of the humble match, he set a new one. Unfortunately, and this is one of the most amusing points about this problem, he had forgotten the answer himself, and at the end of an hour or so, when 11 o'clock came, the answer was still to seek. Luckily the New Zealander remembered that he had in New Zealand a friend on the railways, clever as all New Zealand railwaymen are, so a bet was made as to whether this railwayman could “do it” in three minutes, and in any case the answer was to be correctly set down and posted “Home.”

Some months afterwards the railwayman set to work eagerly on this new enigma, but, alas, he took 3 minutes 40 seconds, and to make matters worse, when he came to write it down a few days afterwards, he, too, had forgotten the answer. So the problem was printed in the Railways Magazine last May, and slowly and painfully from the mass of correspondence that inundated the editor the answer has been arrived at anew.

During the last year the problem has become a “floater.” John o’ London and his readers wrestled with it rather unconvincingly, one American magazine traced its genesis to a Tripos examination at a well-known English University. Here is the problem:-

“There are, on a certain train, a driver, a fireman, and a guard, whose names are Smith, Jones, and Robinson, but not in that order.

“On the train are three passengers, also, Mr. Jones, Mr. Smith and Mr. Robinson. Mr. Robinson lives at Leeds, the guard lives half-way between Leeds and Sheffield. Mr. Jones's salary is £1,000 2s. 1d. per annum. Smith can beat the fireman at billiards, the guard's nearest neighbour (one of the passengers) earns exactly three times as much as the guard; the guard's namesake lives at Sheffield. What is the name of the engine-driver?”

And here, if it be humanly possible to set it down correctly, is the answer:—Since the guard lives halfway between Leeds and Sheffield, and two of the passengers live at Leeds and Sheffield respectively, the guard's nearest neighbour among the three passengers lives at some point closer to the guard's residence than either Leeds or Sheffield. Now this passenger is not Mr. Robinson living at Leeds, nor Mr. Jones, whose salary is not exactly divisible by three for payroll purposes where fractions are rightly disregarded. Therefore it is Mr. Smith. Seeing that Mr. Robinson lives at Leeds, and Mr. Smith at some point nearer the guard's residence, it must be Mr. Jones who lives at Sheffield and has the honour of being namesake to the guard. Now, the names Smith and Robinson are left for the christening of the driver and fireman, and as Smith can beat the fireman at billiards, Smith must be the name of the driver.

Where the traveller's New Zealand railway friend floundered was in deciding whether Smith was a working-man or a passenger. Such a difficulty would never trouble an Englishman; for instance, John o’ London never felt it. If it had not troubled our New Zealander, he would have solved the enigma in 1 minutes 45 seconds. Not so long ago, when the English cricket team tussled with Australia, this valuable distinction was also carefully observed, and even the Bulletin would record that amateur Mr. Smith was clean bowled by Ferris for 6, while professional Jones made 85 not out.

However, the Editor decides that this correspondence is now closed.