"NUTS!"

Evening Post, Volume CXX, Issue 126, 23 November 1935, Page 25

"NUTS!"

Intellect Sharpeners

All rights reserved

(By C. J. Wherefore)

Readers with a little ingenuity will find In this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, It will be found that none will require a sledgehammer to crack them. Address corres|«M«Me tt P.O. Box 1177, WellinftM.

r A FEW SHEEP. A farmer bought a small lot of sheep U at a saleyard, for the reason that he 1 obtained them at a low price. That | was his own explanation of why he took the trouble to bid for only 36 5 sheep and drive them home. But his f schoolboy son says that he sees quite " another inducement. Before making 1 this purchase the farm was carrying t five sheep to every six acres, or as he * describes it, five-sixths of a sheep to the acre. The addition of 36 sheep r converts this fraction into anothei, , i which can also be expressed with one r numeral in both numerator and denominator. The boy also states that ~ r two other men, who might have bought the sheep, would have peri formed similar conversion of the frsc- ■ tion five-sixths into other fractions j equally simply expressed. How many acres are there on each of these three - farms? | THREE BOOKS. A certain lady, who has been a t grandmother for several years, pro-1 L tests that she knows • nothing about mathematics and very little about , arithmetic. For this reason, she considers that her married daughter is very unjust, when she pretends that three books sent as presents were purposely chosen, because the prices were i proportional to the ages of the persons to wliom they were sent. These three persons are, the daughter already mentioned, and a grandson and granddaughter. Her own statement is that she merely went to the shop with the intention of spending one pound, and if anyone at the time had mentioned that the age of the daughter is four times as much as that of the boy, she would have had to refresh her mem-1 ory and make a mentalcalculation before confirming it. Now it is generally known that this firm of booksellers always sell their books at prices, in which the odd pence, if there are any, are 3, 6, or 9 pence, and with this inj formation readers are invited to find the three ages and also the prices paid for the books. DRIVING AND WALKING. Two motorists started from the same hotel to make the same journey and one travelled three times as fast as the other. When this one had accomplished three-quarters of the distance they had to go, his car broke down, and he had to walk the remainder, in which he averaged four miles per hour. The slower man, driving at uniform speed ■ all the way,' reached their destination at the same time as the pedestrian. At what speeds were the two cars driven, and if it is not asking too much, what was the distance they had to travel? AN ERROR IN ADDITION. Professor Aftermath was telling a friend about a little experience he had. "We had to stop at a small township for petrol and a trifling repair, and my wife and four daughters strolled away to look at the shop windows. They returned, saying that they had a mathematical curiosity for mo. Each of them had spent some mon^y, the total came to one pound, and the ' five sums in shillings and pence show-1 ed every numeral from 1 to 9 and 0 without using any one of them more than once." His unenlightened friend ' expressed surprise at ■ such a result i and the professor continued: "Yes it I was a surprising thing to say, especially as that happens to~be impossible Of course, I challenged the accuracy and we found that the five sums spent j were set down correctly, but the addition was incorrect. Still the error w?s the smallest they could have made." Can you remember what the five amounts were?" was the next question. Yes, they came in a systematic way so that I had no difficulty in memo-! rising them." What was'the amount of the error? Also have readers any-1 thing to say about the five individual sums spent? ARMCHAIR PROBLEMS. A carrier, named Charles, .was delivering a load of empty cases, and when he arrived at his destination, he found that 23 of them had fallen off during the journey. He knew that two other carriers were on the road behind him, an«( this is what he said: If. Bill picks them up, he will have twice as many as I have left on my lorry, and if Archie picks them up, lie will have three times as many." For the purpose of the problem, it is understood that no man has less than 10 cases, and the question is how many each of them had. John and Peter were travelling in the same train. Each of them had bought a. book, but neither of them liked the one he had chosen, so they exchanged them. When they finished these books several days afterwards each of them sold the one in his possession for one-third of what the other had given for it, and wrote to his friend to tell him what he had done. One book had cost its purchaser more than the other, and the money which had changed hands at the three places bookstall, second-hand dealers, and the places at which the letters were posted, . amounted to 5i times the difference in the prices paid. How much did the bookstall charge for the books?

SOLUTIONS. Word Change.—Soon, moon, morn, more, sore, some, same, lame, late. Stamps.—One man bought 10, 1, and 2, at sd, 4d, and 3d respectively, the other took 9, 3, and 1, at the same value, again respectively. On Farm.—Allowing for additions to one mob and numbers missing from the other, there were 91 sheep on the road and 130 in the paddock. The man's earnings may have been £17, not more. Sufficient Information.—lt is impossible for one of the neighbours to have three cows less >han P has unless this is true of the other neighbour also. Therefore P has 16 cows, and each of the others has 13. Meeting.—The minority who remembered must have been either 12 or 1 and there is no reason for disbelieving that it was the smaller number. Then 9 sent apologies, and of the remaining 90, one half forgot the date and the other half forgot the meeting altogether. Watches.—The second master is evidently a teacher of English, and realises that Ihe words used do not necessarily imply (hat the price ticket en the cheaper watch showed the other j figures in the reverse order. The an-1 swer is that the watches cost 23s lOd and lls lid. - j