INTELLECT SHARPENERS

Otago Daily Times, Issue 22717, 1 November 1935, Page 2

INTELLECT SHARPENERS

Written for the Otago Daily Times. By C. J. Wherefore. [Correspondence should be addressed to Box 1177, Wellington.] A SIXPENCE WORTH. Three boys found a sixpence on the road. Each one claimed his share, but they agreed to spend the "money at once on sweets and to divide fairly. The first boy obtained a certain number of these for his twopence, the second got six more, and the third received three more than the second. When the first boy counted what he had he made three equal shares, but had one left over. The second boy pooled his lot with the first, but now there were two left over after the three shares had been counted out. The third boy then pooled his lot with the other two, and this time they made three equal shares without any left over. The number each received was not three times, but three times and a-half the number which the first boy had counted out for each share, when he found that there was one left over. How many of them did each boy receive? SIX BOYS. Six boys are accustomed to meeting and playing together on Saturday. They are all of different ages, and the number of years between any one boy's age and that of the next boy is always the same. _ When all six are present the sum of their ages is 66. Last Saturday one of them was absent, and the sum of the ages of- those present was equal to the age of the absent one added to seven times the age of the youngest. What are these six ages, and which one of the boys was absent? TWO SHEEP OWNERS. Ais a farmer. He says he has a certain number per cent, of lambs among his ewes. His neighbour, B, can show a better result, for he has 100 per cent., but his flock is a very small one. In fact. A, with the smaller percentage, has a dozen lambs for every one owned by B, and has actually 539 lambs more than B, which ought to satisfy him. Still he would like to have a higher percentage; even 90 per cent, would be more pleasing. How many ewes and lambs have each of these two men? A PILLOW PROBLEM. A man wanted to plant a number of trees of a kind which he especially fancied, and found that the plot ot ground would hold 100 of them. The nurseryman, to whom he wrote, could supply the trees at a catalogued price, but had not 100 of them in stock at the Lime. The cheque, which the buyer gave for the number of trees delivered, showed in the shillings and pence columns the price paid for each tree, and the number of pounds was one-third of this num.-* ber when expressed in pence. To complete the hundred required, he visitea another grower, and obtained these for twopence per tree less than before. The sum he had to pay this man was easily calculated, because he remembered the value of a certain square, and this enabled him to write down the amount at once. How many trees did he buy from each grower, and what were the prices paid? This is purposely called a pillow problem, because that is a true description of the time and place in which the present writer devised it. SUBSTITUTION PROBLEM. The line given below is an entry on an invoice. The problem is to write numbers in place of the letters, so that the result is correct arithmetic. The values of B and C differ by only 1. (C squared) articles at C pence, fA. B. C. AN EASTERN STORY. A certain great prince required a new man for the post of commissioner of taxes, and there were three applicants. Now one of the most important sources of revenue was a tax on camels, and, the prjnce thought the following question was an appropriate one, as well as being a suitable test of intelligence. A taxgatherer visits a town in which there are three owners of camels. He asks the first one, Ben Hassan, how many camels he has assessable for tax., and the reply is: "If Alibaba had 11 more, he would have half as inany again as I have." He then asus the same question of Cassim, who replies: "If Ben Hassan had IX more, he would have half as many again as 1 have." " Now tell me," he asks, " which of these three men owns the largest number of camels? " The first applicant said the Cassim had the most and Alibaba the least number. The second exactly reversed this, and declared that Alibaba must have the largest number and Cassim the smallest. The third candidate said that all three owners possessed the same number. The prince dismissed all three office-seekers as being incompetent. Why were all three answers unsatisfactory? SOLUTIONS OF LAST WEEK'S PROBLEMS. Paying Debts.—lljd. Word Change.—Bold, bolt, belt, beat, bear, wear, weak. Ages.—There are four children, whose ages make a total of 20, and the sum of the parents' ages is 100. Travelling.—Eighteen pence for each person served. The railway journey must have amounted to 64 out of the 72 miles, and the other result is then easily seen. Eggs.—The maximum number is 12 dozen, and.the minimum is 11 dozen, so that no intermediate numbers exist. The maximum is made up of seven dozen at Hd, three dozen at 13d, and two dozen at 14(1. Bookseller. —The smallest number of books that will fulfil the conditions is 43. It is interesting to notice that we do not know the number of authors represented originally or whether the sale of three books diminished this number by 3,2, lor 0, but this absence of knowledge does not affect the result, 43, given above.