INTELLECT SHARPENERS

Otago Daily Times, Issue 23594, 2 September 1938, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By 0. J. Wherefore Correspondence should be addressed to Box 1177. Wellington. CHARADE These days of long enforced rest and ease, How slow they pass, and then we find too soon, Books, which in evening hours failed not to please, May FIRST us in the morn and afternoon. Yet there be SECOND, whose spells for ever stay, The wizard, Scott, with his own arts somehow, No doubt his tales cheered sick men in his day, And could not WHOLE be e’en then or now. FINANCIAL The vicar required a small sum of money to pay for some repairs to the organ, and he had received a half-promise of a subscription from Mr A. He promptly told Mr B, who is a business rival of Mr A, and is rather jealous of him. Mr Bat once declared that whatever Mr A might offer, he himself would give an amount 20 per cent, greater, Mr C, who happened to be present, is also hostile to Mr A, and he said that no matter what his enemy might give, he himself would give 25 per cent, more. The vicar then returned to Mr A, and made that man believe that he had promised a certain sum, which he named to suit his own purposes. The result was that the debt, which amounted to pounds without shillings or pence, was obtained from the three donors, and there was three pence over to be used for other purposes. How much did each man subscribe? A PASTIME We are all familiar with the process of adding together vulgar fractions, for we cannot escape tjiat at school. But recently, during a period of enforced idleness (in a private hospital, if frankness is a virtue), it occurred to the present writer that it might make a pleasing problem to reverse this process. This means that we are given a certain fraction, supposed to be taken from the answers at the end of the book, and it is required to find the individual fractions of which it is the sum. Usually such' problems are just difficult enough to make them interesting, and here are two for readers to experiment with. (1) Find the fractions which added to-, gether make 1960 over 2117, and (2) those which make 1601 over 1612. TWO SHORT PROBLEMS “ My telephone number,” said Miss Flower, “is composed of three numerals, which make 16 when added together, and it is a perfect square. Both these statements are equally true of my sister’s telephone number, which is nearly twice as large as my own, in fact it would be just twice as large if it had 7 added to it.” What are the two numbers? Both Tom and Mary have accounts at the Post Office Savings Bank, but neither of them owns more than a few shillings. Three times Tom’s money added to four times Mary’s money would come to only one shilling more than eight times Mary's amount. In ; order to make this problem really easy, let it be admitted that one of them has 11 shillings. How much has the other?

ARMCHAIR PROBLEMS I bought a supply of apples, which filled a large bag. When I took them out I found that the fruiterer had given me a few pears as well. The apples were nine times as numerous as the pears, but when I multiplied together the numbers of the two kinds of fruit the product was 9 times 9, that is 81. How many of each were there? A social evening in our township ended with a dance, but this part of the proceedings was not altof ether a success; Two reasons may e given—the first, that the women were more numerous than the men. and the second, that only a limited number of the men were dancers. At one time it was stated that 32 per cent, of the men were dancing, and only 8 per cent, of the women. What percentage of all those who were present were men? SOLUTIONS OF LAST WEEK’S PROBLEMS Geometrical Problem.—One triangle had the sides, 10, 24, 26 feet, the other had 15, 20, 25 feet. Blankets.—There were 48 blankets, which were marked at 15s lid. but he accepted £37 for the line. Payment of Fine.—He had Bs, and borrowed 5s 6d and 6s sd. It will be seen that he might have had as much as 18s lOd, but evidently this is not intended. Crossing River.—The boatload, which included passengers of both sexes, wao composed of three women and eight men. Therefore, the whole party consisted of 66 persons, who crossed in six boatloads, each of 11. Sheep.—lf there were 42 in B and 22 in C, he would need only two from Ato be put into B. The solution that one could be taken from C to make it half of the 42 in B, is ruled out, because the words used show that more than one was moved.