INTELLECT SHARPENERS.

Otago Daily Times, Issue 20004, 22 January 1927, Page 20

INTELLECT SHARPENERS.

By T. L. Bbiton. 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 ot the “nuts” may appear harder than others, it will be found that none will require a sledgehammer to crack them. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. GUNGHA AND COMPANY. Of those who observe the methodical and patient conduct of the Hindu fruit sellers to be seen in various parts of northern cities, few are aware of the bustle and activity that goes on in their large storage shed when the day’s supplies for the hawkers are being adjusted. For most of the sellers find themselves with too much of one kind of fruit anu too little of another, and the bartering and counting that go on amongst them in the early morning make quite an interesting scene, if a noisy one. Gungha, Singha, and Ab-dha were preparing to bart'r at the time I dropped in, and before they commenced I noticed that Gungha had three times as many plums as oranges, while Singha had as many apples as Gungha had plums, and each had an eq l .. ’ number of oranges. Ab-dha had no fruit beyond 24 dozen oranges. He exchanged with Gungha two dozen of these for six dozen plums, and four dozen more were bartered with Singha for six dozen apples. The latter completed the pro. -dure by exchanging with Gungha four dozen apples for eight dozen plums. The total in the "pool” of the three varieties , was 72 dozen, and at the end Ab-dha had four dozen more than Singha and the latter 10 dozen more than Gungha. As Ab-dha had 24 dozen at the start, iwhat quantity did the other two have? WHAT MIGHT HAPPEN. “I hope it will never happen that women become the chief wage earners in the world,” said the 'proprietor of one of the principal city cafes the other day. He saw my look of curiosity and continued: “Outside the dress an' fripperies shops it would mean a big slump in business everywhere, for women as a general rule are great economisers in everything but clothes. Take anv other class of business, and men will always choose better quality goods, consistent with their incomes, and seldom haggle over the prices. The cafe people find it so in a very marked degree, for the average woman does not spend more than 9d or Is,- whereas the average for a man is about Is 6d, and when a lady accompanies him he generally spends up to 3s each.” The speaker was just then called away, and, while enjoying a cool fruit salad, I thought out a little problem. Supposing 25 people are being served, ladies and gentlemen, not as a party. The tables only sit two persons, and some of them are occupied by a lady and gentleman together, the others by ladies or gentlemen separately. At the former tables the gentlemen spend 5s 3d each, gentlemen alone Is 3d each, and ladies unaccompanied by the "‘unfair sex” 9d each. The total amount spent is £2 10s. How were the tables occupied? FROM CASSAR TO OESAH. I was called into a discussion the other evening and asked an opinion upon a little problem that had given some friends material for no end of controversy. One lady stated that all were agreed that the composer’s solution was not right, but could not agree as to the correct one. Here is the problem: X hired a car for the day to go to K—and back, driving him- ■ self and paying £3 for the hire. Exactly halfway he picked up Y who desired to go to K— and back. On the way he inquired the fare and X told him what he was paying for the car, and that Y could pay in proportion. What was the correct fare for Y? One of the party said that four had agreed that 30s was right, whilst five stated that as X travelled twice the distance of Y he should pay twice the fare—viz 1 ., £2 for X and £1 for Y. When I said that the composer’s solution of 15e was correct the look of doubt on their faces prompted me to explain how it was so. “Let us divide,” I said, “the full distance there and back for which £5 was charged into four sections of 15s each. X travelled tire first section alone, 15s, the second section he shared with Y. 7s 6d each, the third was the same as the second, 7s fid each, and her Y left the car, X going the fourth section alone, 155.” Thus Y’s correct fare was 15s. My friends seeing the simplicity of it, put in this way, burst into a hearty laugh. It might have been heartier if they knew they had appealed from Caesar to Caesar. DOMESTIC ECONOMY. When the professor, who had just been told by his wife that the baby had swallowed sixpence, remarked that, owing to the depreciated state of Exchange the sixpence was really not worth bothering about, it did not reflect his true feelings. . The fact is that at the moment he was in the middle of a little problem of his wife’s in domestic economy— a study the professor had persuaded her to take up. It appears she had just bought a quantity of gooseberries at 9d a lb and red currants at Is a lb, and complained that she really required 11b more of fruit for the quantity of sugar she had prepared, and asked the professor to look into the matter, as she did not desire to expend any more money. It did not take him very long fo discover, from a perusal of the bills, that if his wife had divided the money equally between the two kinds of fruit she would have received the exact quantity required —vi".. 11b more. How much did the fruit cost? THREE DAUGHTERS. A widow left £9OOO to be divided between her three daughters, Alice, Kate, and Mavis, in the proportion of i, 1-5, and 1-6 respectively. They were all married, and Mavis, unlike the other two, had married a wealthy husband. She therefore renounced her claim. How should the estate be divided equitably between her poorer sisters? SOLUTIONS OF LAST WEEK’S PROBLEMS. SLEEPLESS NIGHTS. The divisor that will leave the same remainder in each case is 31, 1 remaining after each process. FOUR ABSENTEES. There were 12 in the original party, the eight remaining being called upon to pay 12s 6d each instead of 8s 4d. NO CHANGE GIVEN. One lady’s account was 3s sd, the other’s 7s lid. HALF AS DEEP AGAIN. The hole when finished was 7ft deep. MISS REMINGTON AND MISS UNDERWOOD. The explanation of the solution was given last week, as requested by many readers.