INTELLECT SHARPENERS

Otago Daily Times, Issue 23866, 21 July 1939, Page 3

INTELLECT SHARPENERS

Written Jor the Otago Daily Times By C. J. Wherefore A PAIR OF HORSES Watson wanted one horse, not a pair, and Jones offered to sell him his choice of two he had for sale. But the buyer took both horses, and Jones’s explanation is that they were equally good, so that there was really no choice. When asked about the prices paid, he said that three times the money paid for the first one came to one-ninth of the square of the number of pounds. As to the second one, if the price had been one pound more or one pound less, the numerals which make the squares of these prices’ would add up to the same total. At what prices did he sell the two horses? A FAMINE IN TOBACCO The men camped in a hut in an out-of-the-way locality had been cut off from their usual source of supplies by a river in flood. When the packman arrived, he found the only shortage they had feared was tobacco. On the shelf were several packets of cigarettes, each one the property of a different man. By placing these together in pairs, it was possible to arrange that one member of a pair had one and oneeighth times as many as the other member of the pair, and another individual had one and one-third times as many as his mate. Other such ratios were one and a-half, one and one-fifth, one and three-fifths, and one and four-fifths. And one man of the party remarked that if they shared all their supplies equally there would be exactly so many cigarettes for each man without any fractions. How many men were there in the hut, and how many cigarettes had each one of them? ARMCHAIR PROBLEM The secretary of our Philosophical Society reported a small increase of membership. The subscription is a guinea, but it is usual to admit per sons who are still at the university or at school for 12s 6d. At first our .overworked secretary made the mistake of stating that the new members paying the full subscription were the more numerous, but he had to admit that the reverse was really the case, and that his error was caused by the totals received from the two classes of subscribers looking so nearly the same. In fact, they differed by only two shillings. How many new members were there? SHARING EXPENSES Mr A. had hired a car to take him to a place a few hours’ journey away. On the road, after driving a number of miles, he stopped at the house of Mr 8., who also wished to go to this unnamed place, and they agreed to share expenses for the remainder of the journey This arrangement was upset by the fact that shortly afterwards they had to pick up Mr C., and take him to their destination also. Now that part of the road which A and B travelled together is one mile longer than that which A travelled alone, and the' third portion, over which C was with them, is again one mile longer than the second. In carrying out their intention to share expenses, it will be understood that when there were two passengers, each paid one-half of the cost per mile, and when there were three, each man paid only onethird of it. The owners of the car computed this at the same rate per mile all the way, and Mr A’s share came to £4 2s 2d. What was the length of the journey, and at what once per mile were they charged? THEY MAY HAVE WALKED HOME TOGETHER William had proposed to Florence tnat they should walk to the Post Office for the mail, but she was not in a pleasant mood, and refused to go, so he took his bicycle nstead of walking. When -.he reached the stage of wishing die had said Yes instead of No, she started to walk rapidly, with occasional runs, down the road to meet him on his return. She was makihg good progress in this hurried manner, and had actually completed one-third of the distance at an average speed of six mile per hour, when a neighbour overtook her, and carried her in his car the rest of the way at 18 niles per hour. These two happy individuals arrived at the P.O. at the same moment. At what speed had William travelled? SOLUTIONS TO LAST WEEK’S PROBLEMS A Journey.--The answer is 54 miles, the half of 9 times 12. Books.—The damaged copy cost only 2d. Six new copies cost 4s Id each, and two second-hand Is 2d each. Puzzle in Words. The three words are: Shingle, Strenuous, Roused, and the word made with the fragments is Ingenuous. Short Problems. —(1) Yesterday 16 for lid, to-day 17 for a shilling. (2) There were 12 blue flowers and 11 red ones. With this information readers will prefer to find for themselves how many white flowers there were. Problem in Ages.—lf we can believe that a little girl aged 5 would behave in the manner described, there is an easy solution at once. It seem” preferable to suppose tha 4 she is 16 years old, and her mothe, 39. Then the piece of ribbon in the drawer contained 5 yards, so that the job required 60 yards.