"NUTS!"

Evening Post, Volume CXXII, Issue 70, 19 September 1936, Page 24

"NUTS!"

Intellect Sharpeners * All rights reserved

(By C. J. Wherefore)

Readers with a little Ingenuity will And 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 correspondence to P.O. Box 1177, Wellington. A CHEQUE IN SETTLEMENT. A storekeeper was compelled to accept a cheque for £9 in settlement of an account owing to him for less than £l, and he made a charge of one shilling for cashing the 'cheque. He also made his customer accept two cheques, one of which was for an exact number of pounds without shillings or pence, and the pther, which Jaad, evidently been used for paying some subscription, was for a number of guineas. In fact, the only cash he handed over was one £1 note. His accountant, having his attention drawn to the matter, noticed another remarkable fact, namely, that the amount shown on one of these cheques was exactly three guineas more than the sum s of the amount owed to the store and the £1 given in the change. For how much was the storekeeper's account .thus settled? / ■ ARMCHAIR PROBLEM. Mr. S. had bought' some fowls, and was driving home in a spring dray with his purchases in a box. He overtook Mr. T., who was driving a mob of i sheep, of which, the total was 2 more than 32 times the number of the fowls, and as his friend was in difficulties making his sheep cross a bridge, Mr. S. left his seat and gave what assistance he could. His horse was impatient and crossed the bridge-in the midst of the mob, with sheep both in front of him and behind. Now there was a toll which was charged on all livestock using that bridge, and the humorist w,ho collected the money reckoned that the fowls, which had been in the middle of the mob, must be part of it, and' charged for them,. making them 3 per cent, of the whole number. How many fowls had Mr. S. in the dray? A QUESTION OF SHEEP AND ACRES. 4 "You must have a sheep to the acre in that paddock," said the man who was content to express his ideas in round numbers. "A little more than that," was : the reply of the precise farmer, iwho the sheep, and after spending a few seconds in mental arithmetic, he informed the ques' tioner that there were 12 sheep on every 11 acres. "V«ry, well," said the careless speaker. "If you put these 26 sheep you have in front of you into the paddock with the others, you will have three sheep .to the acre." But the reply was: "Not at all. I should have to put these sheep and a quarter of*a sheep more among them to make the mob three times the number of acres." How many sheep had he, and how, many acres are' there in the paddock? / A CROSS-ROADS PROBLEM. A motorist stopped at a cross-roads 'to examine his supply of petrol, which seemed to'be running short. He was travelling northward, and he knew how far behind him was the last refilling station he had passed, and also how far ahead was the next one. What struck him as a remarkable coincidence was that, if he had been travelling on the road from east .to west,, the distance between two stations would be the same as that between the two on the road he was now following. But the amount of road space between the westward and. northward stations, passing through the crossroads, of course, was twice as great as that between the southward and eastward stations, measured in the same way. Which 'was the nearest plac,e at which he could obtain petrol, and at what distances from the crossing were the other supply stations? "•' ■ . THE WIDOW'S LEGACY. This is admitted to be an improved version of a very old and out-of-date problem. ■ A man died leaving a will in which he stated that his entire fortune came to £BOOO. He had four sons, to each of whom he left twice as much as he left to his widow, and five j daughters, to each of whom he left three times as much as he left to each son. The money was found to be less than the amount anticipated, and the result was that the widow receiv!ed an exact number of pounds, instead of a complex amount,of £.s.d., plus a fraction of a penny, as in the original version of this story. In fact, iif there'had been no will giving these extraordinary instructions, it would have been possible to give the same amount in pounds to each, beneficiary named, and also to one other, who would have had a. claim on the estate. How, much" did the widow receive?

A JOURNEY BY ROAD. A man started to walk a distance, which was an exact number of miles, but he had no intention of performing the whole journey on foot. When he had walked only a few of these miles, he begged a lift on a bus, offering a shilling, and asking to be carried as far as that money would suffice to pay for. The driver, however, took him to his destination, and laughed when he remarked that it was not an extravagant rate per mile which had been paid. In this, he mentionel a coin in common use, but -the traveller told his friends that the whole journey had worked out at three-sevenths of a penny per mile. What is the length of the w,hole journey, and how many of these miles did he walk? 1 SOLUTIONS. Word Change.—Sick, silk, milk, mill, will, well. Cyclists and Pedestrians. The cyclists rode first 23 miles, then 22, and then 15 miles. Armchair Problem.—There were 20 flowers in the first vase and 25 in the second. They must have been tied up in bunches of 5, because 25 is the square of this number, and has no other factors. Booking Clerk.—The amount to be paid must be 713 pence, not 727, because the latter is a prime number. The former is the product of 31 and 23, therefore the fare is 2s 7d. Daughter.-rTne school. girl is the daughter, and she is 15 years old. The alternatives are 4 and .26 years. The first must be rejected,, because it is below school age, and the/ last is obviously inadmissible, because Mrs. J. is not old* enough to be the mother of a woman aged 26. Centenarian—The total number of children must be 3 or 9. or 11 or 33, these being the factors of 99. The smallest cannot include, both girls and boys in the plural, and there is no solution with 33. If there are 9of them, the answer is that 7 boys receive £lO and 2 girls receive; £ls. If there are 11, then 7 boys get £8 and 4 girls get ill. In either case there are 7 boys, and this is.the only question asked. ■' ,