INTELLECT SHARPENERS

Otago Daily Times, Issue 23353, 19 November 1937, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C. J. Wherefore Correspondence should be addressed to Box 1177, Wellington. AN IDYLLIC PROBLEM “ How many acres did you say there are in this paddock? ” I asked my host’s daughter, “Do you see those sheep over there under the willows? ” she asked me in reply. “ Well, if there were seven more of them, there would be one sheep to the acre.” “ I make the number 40,” I told her, “so I suppose there are 47 acres.” But she shook her head, and told me there were more than that. “Last week my father had the cows in here. Their number was only a fraction of the number of those sheep,” and she told me the fraction, but that is part of the problem, so I omit it. The clue she gave me is that if there had been 11 more head of cattle in the paddock, that would have made just one to every two acres. What fraction did the lady specify, and how many acres are there in the paddock? ANOTHER RIVER-CROSSING PUZZLE Mr F, the ferryman, charges a fixed amount for taking single passengers, but when he has to deal with parties, no one can understand the system on which he computes how much he will demand. A few days ago he had to take one party across the river from north to south, and at the same time he had to bring another from south to north on the return crossings. ' Both of these parties were much too large for one boatload, and the charge for the trips from north to south was 6d for each load of eight passengers. When he returned with the others, he carried 13 persons, and charged lid. The money was paid when the passengers disembarked, and the total of it came to nine shillings. He made no crossings with less than the numbers stated. On which side of the river was he when he received the last payment? SUGGESTION FOR A SHORT STORY Mr Dull’s secretary was absent from the office owing to illness, and her younger sister was sent into his room to take down his correspondence. She is only a very little younger than the absentee, and is remarkably like her, and several of those in the office were ready to bet that their employer would not notice the difference, as he is rather short-sighted, and hardly pays any attention to any of the younger members of the staff. lam informed that those who bet on Mr D’s inattention won their money. But when I asked some questions about the ages, they thought I was on my usual business in search of new problems, and this is what they told me: The product of the ages of the sisters is six times Mr D’s age, but his age, which is an exact multiple of the age of the younger girl, is not a multiple of that of the elder one. What are the ages of Mr D and of the two typistes? EXCESS LUGGAGE This is another old problem with some additions, which make it worthy of being set before presentday intellects. Mr Traveller, on the point of starting on a journey, found he had to face a bill of 6s 7d fbr excess luggage. He was about to pay this, when he found Mr Longway was bound for the same destination without any luggage, and this friend in need offered to take the excess luggage as his own, so as to avoid the heavy payment. It was found, however, that the amount was 3001 b, and was still too much for one man, so a third person, Mr Faroff was suborned into dividing it with Mr Longway. The result was that Mr T. paid only 4d, while the other two paid 9d and lOd. For the purpose of the problem it is supposed that the charge for excess luggage is at a fixed rate per lb, and the two questions asked are: What weight of luggage was there altogether, and how many lbs does the department allow each passenger to take free of charge? A HIRED CAR Four men hired a car to take them to a distant town, where they had business together. Mr A fetched this car from the owners, and drove as far as Mr B.’s house, where he picked up his friend. Mr B drove it to Mr C’s house, and this distance is 25 per cent, longer than that in which Mr A was driving. Mr C drove to Mr D’s home, and Mr D _ drove the rest of the way, making his own share 20 per cent, longer than that of Mr C. Up to this point the car had driven 108 miles since it left the owner’s garage. On the return journey one of the four men drove it for just half as many miles as he had driven it before, and the arrangements were such that he had just reached his own house, when he had finished his spell of driving. No one of the four was carried past his own house, on the contrary one of them ceased driving when he had still 23 miles to go before reaching his home. How many miles did each of them drive this car on both the outward and return journeys? SOLUTIONS OF LAST WEEK’S PROBLEMS Problem in Ages.—A is the mother, aged 49, C is her son, aged 29, and B is the unmarried woman, aged 39. Simple by either arithmetic or guesswork. Choice of Roads.—lf we accept the suggestion that the town is not far away, the distance is 10 miles by the ford and 16 miles by the bridge. Substitution.—The coin not included was sixpence. Thus, halfcrown, two-shilling piece, shilling, threepenny, and penny, make 5s lOd. C bought five packets at 14d. and J bought five packets at lOd. Three Fishers—This is only an armchair problem crowded out of its place under the other headline. B and J claimed only five and seven fish, because if they had claimed more it would mean that R caught nothing. It is easy to see that each man invented three fish. Armchair Problems.—(l) This is easy, because if C is pore expensive than D, its value cannot be less than £33, while D cost £3l. It follows that A cost £29 and B only £7. Other solutions are possible, if there is no objection to making B even more worthless. Of course, if C cost ££4o, then B becomes 0. (2) Not exactly but she is either 23 or 24 years old.