INTELLECT SHARPENERS

New Zealand Herald, Volume LXXII, Issue 22250, 26 October 1935, Page 5 (Supplement)

INTELLECT SHARPENERS

By C. J. WHEREFORE

REPAYING A DEBT Jones owed Smith four shillings. They were playing cards for farthing points, and Jones was winning, so Smith suggested that this was a good time for his opponent to repay part of his debt. To this Jones replied that, if he won on the next game the value of the counters he held at that moment, he Mould pay one of the shillings he owed. He did so, and also undertook to do the same again on the same conditions. When this had happened four times, Jones bad paid off his debt, and had no money left. How much had he when the agreement as to conditions of payment was made;' WORD CHANGE In the lines given below the spaces are to be filled with a series of words, each of which differs; from the oue before it by one letter, making the lastword entirely unlike the first, and with quite the contrary meaning:— He was not , and he had no skill, But he managed the on the door, His plan was merely to rob the till, Which held about two and four. But a full-sized man with his filled tight, Whose was the street in view, Was passing the shop at that time of night, And he heard a sound, and he saw a light. That could some -o-atckirLg: too, I would not your patience out By telling a lengthy tale, But, the man's defence is so , that I doubt If he'll keep himself out of gaol. PROBLEM IN AGES The following problem is proposed by a correspondent writing from Opotiki. At first sight it looks as if a large number of solutions might exist, but this is a mistake, because there is only one. At the present time the sum of the ages of Mr. and Mrs. Atkins is five times the total of the ages of their children added together. Two years ago the parents' total was eight times as great as the children's total, and in ten years from now it will be only twice as great. How many children have they ? TRAVELLING EXPENSES Philip had to make the journey from Anthill to Beehives, a distance of 72 miles. He was able to travel most of ihe way by train, and this cost him two pence per mile. When he left the train, he entered a service bus, but in it he met his friend, Bobert, who lives at Anthill, and he was going only part of the distance, in fact to a place where he had left his car to be repaired. Philip left the bus at the same place as his friend, and this stage of the journey cost him seven pence per mile. Robert drove him the remainder of the wav. and this would have cost him nothing, if it had not been for the fact that they had lurjeh before starting, and Philip paid for both. Allowing for this small item, this last stage of the journev cost Philip nine pence per mile, and" his total expenditure was sixteen shillings. What was the charge made for lunch? EGGS BY THE DOZEN A certain firm of provision dealers is accustomed to supplying eggs in three qualities, fresh, new-laid, and guaranteed The second of these costs two

pence more than the first, and the lastmentioned costs still one penny more. Also they do not sell fractions .of dozens. These prices are quoted in penT: only, but it happens that the mean price per dozen is just over a shilling, and that the extra portion is a fraction, two-thirds of a penny in fact. The manager of this business returned after a brief absence, and found his assistant using the office stationery and pencils to work out a little pastime on his own account. Evidently he is something of a problemist, and in reply to inquiry, he explained that he had just supplied two customers, each of whom required twelve shillings worth of eggs, and had selected some dozens of all these varieties. One of them had taken the maximum number of eggs obtainable under these conditions, and the other the minimum number. The manager, while sitting down at his table to desl with the morning mail, remarked simply that now his second ircommand could sell a few more such numbers intermediate between maximum and minimum. This problemist hastened to state that this is impossible, but the manager was now busy with his letters, and paid no attention. How many eggs of each quality were supplied to each customer, and why was the last suggestion an impossibility? BOOKSELLER'S PROBLEM A Lad a number of books, considerably over two dozen, and written by several different authors. He offered these at reduced prices, and soon sold three, after which the remainder showed eight books by each of the authors present among them. Now he transferred these remaining bookß to several smaller shelves, each of which held the ;:ime numbr of bocks, and this he could not have done before Helling the three as described. How many books were there? LAST WEEKS' SOLUTIONS Wireless Set.—There is only one available number, which is a multiple of guineas, shillings, and halfcrowns, and that is £5 ss. The other two are easily seen to be £4 IDs and £8 ss. Argument in a Car.—The velocity of the bus is to 2S as 4 is to 2J, which gives nearly 45 miles per hour. The car would pass 900 spaces in an hour, and 28 miles divided by this number gives nearly 55 yards. Walking and Cycling.—A walks nineseventeenths of the distance before meeting B, and this is 10 and tenseventeenths miles. The cyclist's journey is to A's as 13 is to 4i, which gives 30 aud ten-seventeenths miles. The amusing point is that this problem is easy just where difficulties might be expected. Seats at the Pictures.—Elisabeth went to the pictures on Friday nie;bt wit one other person. The argument is rather long, but it shows with certainty that in the previous visit the sisters occupied seats numbered 9 and 13 in a party of 10 persons. The other result follows obviously. Armchair Problem.—(l) 1, 5, 6, and 12, 1, 2, each making 15. (2) After the breakage described above, the only opposite numbers on one piece are 3 and 9. These with 10 and 8 make 30. (3) The numbers of pence could not be even, nor could they be 3 or 9. Therefore the sums were £3 4s sd, and £5 6s 7d, and no arithmetic is necessary.