PUZZLES OF THE THREE TRAVELLERS

Dominion, Volume 22, Issue 72, 18 December 1928, Page 33 (Supplement)

PUZZLES OF THE THREE TRAVELLERS

Exclusive to The Dominion

By

HENRY E. DUDENEY.

(Author of “Modern Pussies," "The Canterbury Pussies," etc.) (All Rights Reserved.)

ND I find that my friend had married his w’idow’s sister,” said Mr. Andrews. The occasion of this remark was a pleasant little gathering of five persons round the big fire at the Railway Hotel at Tinkleminster on Christmas Eve.

The company consisted of three commercial travellers, Andrews, Benson, and Carew, with Mr. and Mrs. Daniels, their host and his wife. It must not be thought that the three travellers were homeless or willingly away from their families on such an occasion, but for various reasons connected with their work they were so stranded and making the best of their circumstances. They had fared well at the host’s sumptuous table, and were by now engaged in very pleasant conversation. Andrews had just been telling an interesting story of his experiences which ended with that little statement, “And I found that my friend had married his widow’s sis-

ter.” “Is that a legal marriage,” asked Mrs. Daniels. And they all began to think, until Mr. Benson burst into loud laughter and cried: “My dear fellow, if a man’s wife was a widow he was dead, and such a thing is impossible.” “On the contrary,” said Andrews, "it is perfectly true.” "Come, come,” said Carew, "that last glass has got into your head. Andrews.” But they were all amused when, in the end, he explained that the sister was his first wife, that his widow was his deceased wife’s sister. It is curious how this little jest set them off on propounding a series of puzzles that kept them well entertained until they retired for the night. Some of the best of these posers it is now proposed to record for the amusement of the reader. The Six Matches. Benson took four matches from the box and held them on the little table beside him in the way shown In the illustration. “You will see,” he said, “that I have placed these four matches with every match touching every other

match. Can yon do the same with six matches? Of course, you are not allowed to break or bend any match.” They all tried at this little puzzle for some time without success, and in the end Benson had to show them a very simple way in which it can be done. Horses and Bullocks. “I was talking to a friend of mine, a dealer, the other day,” said Carew, "and he gave me this little poser. He said that he bought a number of old horses at £l7 4s. each and a number of bullocks at £l3 ss. each. He then discovered that the horses had cost him in all just 335. more than the bullocks. He asked me if I could, tell him the smallest number of each kind of animal that he must have bought.” . “That ought to be easy, I should think,” said Daniels. But Andrews, who had began to figure it out on a piece of paper, insisted that it would be found a little more difficult than might at first sight appear The men then set to work at it, and Benson was the first to get the correct answer. The Subscription Puzzle. “As we have got into puzzling arithmetic,” said Daniels, “I should like to see what you men can make of this. Men in my trade were getting up a subscription—no matter for what purpose—and six hotelkeepers gave £lO each. As I was particularly interested in the cause, I gave £3 more than the average of the .seven of us. Now, can you tell me how much I subscribed ?” This did not give them much trouble. The Entangled Scissors. Mrs. Daniels here fetched a large pair of scissors, and, producing a long piece of stout cord, she wound it in and out in the 'manner, shown in our illustration. ■ “See if yon can take off the scissors,” she said, “without my letting go the ends of the string.

after another of them tried- to disentangle the scissors.,, In the end she had to show them how it is done. The reader, in his attempts, is cautioned to allow sufficient length of 1 string and to be very careful to avoid twists and tangles, or he will get it in a hopeless muddle. Even when he knows how to do it, the performance requires the exercise of some little care. The Ambiguous Clock. “I have noticed,” said Andrews, “that some cloekmakers are very careless in using two hands so very much alike that they are hardly distinguishable. In fact, I once stopped at an hotel where a clock had two hands exactly alike. Now, if this clock was set going at noon, when would be the first time that it would be impossible, by reason of the similarity of the hands, to be sure of the correct time?” "I suppose,” said Carew, “that you accept the convention used in all these clock puzzles that it is possible to indicate fractions of seconds?” Andrews agreed, and Benson, who was by far the best arithmetician in the company, gave them tile correct answer. Ways of Voting. “I was stopping some little time ago,” said Carew, “at Campchester, which is on my road, and I found some of the inhabitants very interested in this little puzzle that confronted them. The Town Council were taking a ballot of the town in regard to their Corporation Bill, and the ballot paper was arranged in this form.” He produced a paper, of which we here give a facsimile. “The clauses were printed in full, but you do not need them. They

wanted to know in .low many different ways it is possible for a man to vote. For each of the three clauses a man can, of course, vote either for. against or not at all.” This is, of course, quite easy, but there is just one little point on which the reader is likely to trip, and some of the company missed it. The Ribbon Puzzle. “A strong line in my business,” said Benson, “is ribbons. Here is a puzzle in question put to me the other day by a chap, and the answer gave me a good deal of trouble, until I hit

■ on a rather simple way of getting at it. a I have a roll of ribbon Bin. in diameter, and in the centre of the roll ■ there is an open space 2in. in diaf meter, like this." (He drew our dia--1 gram). 1 “Now, as the ribbon is, say, 1-250 of s an inch in thickness, what is the 3 length of ribbon in the roll?” 3 * “Would not the answer depend, asked Andrews, “on whether the ribbon was tightly rolled or not? If loose, of course, the roll would be , much larger than if tight” “Quite so,” said Benson. “But we i will assume it is perfectly tight and ■ ignore any spaces between, and it will i be sufficient to get the answer to the . nearest inch.” i They found this a rather hard nut, ; so Benson showed them his way of , getting at the answer. An Old Enigma. “Here is a thing,” said Mr. Daniels, “that I got from an old book when I ! was a young man, and I have never forgotten it.” A hundred and one by fifty divide, And if then nought be rightly applied, And your calculation agrees with mine Then the answer will be one taken from nine. Carew found the old answer to this enigma, but Benson worked out a new and totally different answer. Perhaps the reader may like to find one or both of these. Upside Down. “Here is an amusing little thing I was shown the other day,” said Mrs. Daniels. “If you write the word “bung” and turn it upside-down it reads just the same. Can you find a

word of five letters in ordinary writing, without any capital letters, that will do the same?” Nobody succeeded in solving this little puzzle so Mrs. Daniels had to show them the answer. Absurd Queries. “Sometimes,” said Mr. Daniels, “people will ask questions that are amusing on account of their utter absurdity. A man at piy bar the other day put to me the question, ‘When is an apple-pie?' Of course be was unable to give the answer, so 1 told him that people shouldn't ask riddles if they didn't know the answers. Then I informed him to his surprise, that an apple is pie when it is cut up in a deep dish and baked with pastry over it.” “I was once asked,” said Andrews, “what it is that you cannot on* up a chimney up, or down a chimney up but you can put up a chimney down, or down a chimney down. Of course, the answer was an umbrella.” “Then there is the old question.” said Benson, “which has. most eqs. a horse or no horse? The answer to this is 'No horse, because a horse has four legs, but no horse has ten legs.’ ” “A woman once told me.” brokj in Mrs. Daniels, “that she had a r,»«ecoloured cat with cherry-coloured spots, and I told her she should not talk such nonsense. Then <h? asked me if 1 had never heard of white roses and black cherries.” “But 1 object,” said Benson, “to the sort of catch like that in which you

are told the story of a donkey that was faced with something quite impossible. When you are asked, ‘What would you have done?’ and you reply, ‘I give it up,’ you are then answered with, “That is what the other donkey did.’ ” “I also object,” said Carew, “to that sort of thing. I know a little girl who has been trained by her parents to put this kind of question to longsuffering visitors. ‘A train went from London to York. Ten passengers got in and free got out. Got dat? At de next station firteen got in and one got out. Got dat? And at de next station seven got in and nobody got out. Got dat?’ When you have finished your patient figuring she asks. ‘What was the name of the guard?’ ” They all agreed that this sort of thing was intolerable, yet the fact remains that they laughed. Such is human nature! A New Cross Puzzle. Then Andrews drew a symmetrical Greek cross similar to our illustration, and said that a good puzzle was to cut it into five pieces so that one of the pieces should be a similar symmetrical

Greek cross entire, and so that the remaining four pieces will fit together and form a perfect square. Carew, with whom these dissection puzzles were a sort of hobby, was -he only one of the party who found the solution. A Tiny Magic Square. Mr. Daniels brought the little symposium to a close with this quite easy puzzle. He asked them to write in the three figures, 1,2, 3, in the square in this order in i row horizontally.

Then put -own two more rows of the same three figures (in any order) so as to form a magic square, the columns, rows, and two diagonals all adding up alike. SOLUTIONS. The Six Matches. The illustration shows the simple way to place rhe ix matches so that

every match somewhere touches every other match. j ]

Horses and Bullocks. The man must have bought 252 horses for 3445. a piece, and 327 bullocks at 2655. a piece, and the horses would then cost him in all 335. more than the bullocks. The Subscription Puzzle. Daniels subscribed £l3 10s. Add this to the £6O from the other six men and we get £73 10s. The average is therefore one-seventh of this £lO 10s. So that Daniels subscribed, as he said, £3 more than this average. THE ENTANGLED SCISSORS. The puzzle is solved by working that loop near the middle of the scissors ’ backwards along the double cord. ' First slacken the string throughout so I as to bring the scissors near the hand , of the person holding the ends. You must be careful to make the looi> follow the double cord on its course in ' and out until that loop is got free of the scissors. Then .ou pass the loop 1 right round the points of the scissors and follow the double cord backwards. The string will then (if you have been very careful) detach itself from the ' scissors. The Ambiguous Clock. The first time wouk. be 5 5-143 minutes past 12, which might also (the hands being similar) Indicate Ihr. 0 60-143 minutes. Ways of Voting. For each of the three clauses there are three ways of voting—for, against, or not at all. For each of the three ways of voting for Clause L there are three ways of voting for Clause 11., consequently. 3x3 equal 9 ways of voting for the first two clauses. Then, as there are three ways of voting for Clause 111., for every one of these nine ways there are 3x9 equal 27 ways of voting in all. But this is not the correct answer because it includes the case where we decline to vote for any one of the clauses. This case must be deducted because the question was, “In how many different ways is it possible for a man to vote?” and not to vote at all is obviously not a way of voting. Of course, to vote both for and against is really not voting at all. The correct answer is 26. The Ribbon Puzzle. Imagine the roll to pe composed of a series of concentric rings of ribbon. As the ribbon is l-250in. in thickness there will be 750 of these ribbon rings in the 3in. thickness. The circumference_ of the smallest ring is 6 ; 2b31553in., and that of the largest ring is 25.1327412 in. Add these together and multiply by 375 (a half of 750), and we get the result 11780.972445 in., which is 327 yards Oft. 9in. —the approximate length of the rolled ribbon. An Old Enigma. The word is C L I O. First write down C I (a hundred and one), insert the L (by fifty divide), and we get C L 1, to which the O must be applied, giving us C L I O (one taken from the nine Muses). Benson’s second answer was this:— 101 90 + 11 — to which add O and 5C 50 we get 90 + 110 =4 = one taken from 50 the nine digits. Upside Down. The word that Mrs. Daniels gave them was

“Chump,” which written as we have here shown reads ,’ust the same upside down. A New Cross Puzzle. If we cut out a smaller Greek cross in the manner shown in the diag-am I, the four pieces A. B, C, D, will fit together and form a perfect square as