INTELLECT SHARPENERS

New Zealand Herald, Volume LXXII, Issue 22142, 22 June 1935, Page 5 (Supplement)

INTELLECT SHARPENERS

SUBSTITUTION In the words given below numerals are to be written in place of tbe letters, so that the result is a sum in simple addition. No two letters have the same numerical value. To make a nonmathematical puzzle, add the word AND, then shuffle and rearrange all fifteen letters to form the name of a book, from which these words were derived. COAL GA I N TI N S

ARMCHAIR PROBLEMS A man put a few sheep into his yard and counted them. If there bad been 23 more, there would have been as many as he had in Paddock No. 1, and if there had been 26.less, there would have been as many as in Paddock No. 2. Now the number in one of these paddocks was an exact multiple of the number in the other. How many sheep were there in each of these three mobs? Four men who were driving along a country road saw some sheep in a small paddock and tried to count them, or at any rate to estimate bow many there were. The driver, who had little time to give to them, stated a certain number. The man beside him was sure there was one more than that, and the man behind him said there were 3 more than the second man had counted. Tbe fourth man's number was 2 more than that of the third. Two of these men had confidence in their results, because they said they had seen tbe sheep in five groups each of the same number. The driver confessed he had not looked at them, and his number was merely half the number of miles per hour read from the speedometer at that moment. The four guesses added together came to less than 90. At what speed was the car driven ? MOUNTAINEERING Mr. Jones was one of a party which climbed a difficult peak. He sent his photographs to the editor of an illustrated paper, and received a cheque which was tbe equivalent of one penny for every 18 feet in the height of this peak above sea level. Mrs. Jones accompanied tbe climbers for only a Ehort distance; in fact, the place where she stopped was 3024 feet below the summit. Here she painted a water-colour, which was shown at an exhibition, and sold for the equivalent of three times as much money for every foot of altitude as that realised for her husband's photographs. What was tlie height of this mountain, and how much was paid for the picture and for the photographs? A CASUALTY LIST The following problem is a modification of one suggested by a correspondent who writes from Auckland. In a war between two small states the general commanding the invading armv was defeated with casualties amounting to one thirty-third of his men of all ranks. He received 2623 reinforcements, made the total under his command 12,319 of all ranks, but this did not save him from being surrounded and compelled to surrender. In the interment camp the prisoners were divided into companies with a little more than 100 in each. How many men had the general before his first defeat and how many companies were formed in the prisoners' camp? NINE SCHOOLGIRLS This problem is intended to be solved in the ordinary way, but it also serves as an introduction to another problem, which was published originally in 1851, and has acquired an historical interest because of the mathematical work published on the subject. Nine schoolgirls were taken out walking on four consecutive days in groups of three, and

By C. J. WHEREFORE

during that time no girl walked in a group with any other girl more than once. In the original problem there are fifteen girls to be arranged in groups of three for seven days. A book, which the present writer was privileged to borrow recently, gives eight pages to the subject, together with footnotes referring to the work of other authors. When there are only nine girls, as given above, the problem of grouping them is not more than pleasantly difficult. LESSONS IN DRIVING When Mr. Somebody bought a second hand car, which was intended to be for the use of his family as well as himself, he thought it a good idea that they should all give an exhibition of their abilities as drivers. For this purpose he chose a road leading to a town a certain number of miles away, where every mile was marked by posts beside the road, and he himself and each of the others drove for the same number of j miles. This is his description of what j happened. "We took an hour and ; twenty minutes to drive there and back. I 1 should have preferred to go a greater j distance say, 50 miles or more. My eldest daughter showed herself a pro- ; ficient driver, but Tom is the real expert, having had a good deal of experience with other persons' cars. His turn came in tbe middle, so that h<> drove into tbe town and back again to the place where he had taken the wheel from Muriel. To show what he could do. he turned round exactly at the mile post, which was very far from being a convenient place for the purpose. He is in the habit of doing this kind of thing, and perhaps it is fortunate that his sisters have formed an alliance to squash him occasionally, otherwise he might be a very conceited young man. We all got the car to go at the same velocity, as shown by the speedometer and also by the time we took over the distance. The previous owner had promised this, and although he quoted merely a round number, it was entirely correct." For how many miles did each person drive the car-' LAST WEEK'S SOLUTIONS Armchair Problem. —It is his twentyfirst birthday. Game with Counters.—A, B, C, D, and E have respectively 78, 90, 101, 111 and 120 counters. The last speaker is D, who requires 6 to make his total half as much again as that of A. Problem in Words. —In Group 1, Snow, none, once, week. In Group 2, Star, tire, arts, rest. The order in which they come in the verse is now easily seen. Guaranteed Easy.—The individual who promised an easy problem has made it clear that only multiples of seven can be used, otherwise the problem is impossible. The answer is 21 boys, 28 girls. Alleged Mountaineers. —There are at least three solutions, but they agree in showing that the girls sat down at the foot of the hill, and it is already clear that this is what they did. The solution most easily found is that the writer of the letter climbed 5 feet, Lucy 10 and Elsa 20, in which the height of the hill is 600 feet. Argumentative Problem.—A and C are marned men, and S and T are mentioned with the pronoun " his therefore R is the only woman, and she must, be the owner of the terrier, which is in need of a manly handling. As this terrier is jealous of the colHe, because its owner pays attentiun to the collie, it follows that this must be the dog belonging to T and left in a sister's care. S was fined for not registering his dog, and this must be one of the numerous expenses imposed when the Alsatian got its owner into trouble with the police. Tbe remaining two are A and C, and as A's wife covets the retriever, which does not belong to her husband, it follows that A owns the spaniel and C owns the retriever.