Intellect Sharpeners

New Zealand Herald, Volume LXXI, Issue 21876, 11 August 1934, Page 5 (Supplement)

Intellect Sharpeners

TWO TILED FLOORS BY C. J. WHEREFORE Two men were sent by a firm of decorators to lay tiles in two adjoining houses. Both floors which had to bo covered were rectangular and the number of tiles supplied for the two jobs was 774. These two men, when they met one another at lunch time, compared notes and found that their jobs were similar in only one small- detail, namely, that the length of each floor was three tiles more than the width. The larger floor had six tiles more than the smaller one both in its length and its breadth. If one man was expected to take seven and a-half hours over the smaller job, how many hours may it bo expected that the other man will require to finish his work?' OBTAINING A LIFT A boy started to walk ten miles and reached his destination in three and a-half hours. But ho cannot walk faster than two and a-quarter miles an hour, so his brothers and sisters are sure that he got a lift for part of this distance. He himself refuses to give any information, but they have fcund that a motor-lorrv passed along the road and that it was driven by a personal friend. This lorry is capable of travelling at 15 miles per hour, and if the supposition of the family about the boy obtaining a lift is correct and the lorry moved at the velocity stated, the question is what distance did it carry him ? WORD CHANGE In the lines given below the spaees are to be filled with a series of words, each of which differs from the one before it by one letter, making the last word altogether unlike the first and with an entirely different meaning. I owed a friend a letter, and I knew not what to think. For in my no thoughts of him I had, I shook my fountain pen and found it • a little ink, And drew some silly pictures on my pad. And. bo I wrote to 6omeone else, and then ideas came. One letter could not hope to them all. Affectionately Yours, I wrote, and signed my christian name. And tried to the letter neat and small. Now here's a letter from her, which the postman brought to-day. Some for thought I find if. givea me too. For at the a postscript is the truth, I grieve to cay. You ought to write more letters than you do. COUNTING TEE DUOKS Two men driving along a country road passed some ducks iu a paddock. Some of these were swimming on a pool of water and the rest were on dry land beside the pool. The man at the wheel said to his friend, " You can count the ducks on the water and I'll count the ones ashore." Then ho put his foot on the accelerator and passed them at his best speed, so that the counting had to be done rapidly and with some difficulty. But the most confusing part of it was that two of the ducks canio- out of the pool while the counting was in progress, and neither of the men could say with certainty j whether or not their counts had in- | eluded these two. The totals they ; had found were to one another as four ! is to five. But it will be seen that there aro really four possible cases. Two of them would give correct re- ; suits, namely, if the driver or his i! friend had included these two ducks ; and the other had omitted them. The ! other two possibilities are that both • had counted them or that both had ' overlooked them. A few yards down i the road they stopped at a house which was evidently the home of the owner of the ducks, but could only j question a young girl at the gate. She knew that there had been 40 ducks originally, but that two or : three, not more, had strayed away. ! How many ducks were there and had | these men counted them correctly? AT A FLAG STATION | A railway station is at such a dis- | stance from a large town that the cost j of a. ticket to this town can be paid | by handing over one silver coin and | receiving one penny as change. It is ; only a flag station, bo that the tickets j have to be obtained from the guard, and sometimes he finds it difficult to | supply the necessary change. This was especially the case one day, when ; the number of persons who joined the I train here was unusually large. The result was that none of them could be j given the penny which belonged to ! them and the amount of money in the ! possession of the guard when he reached ! the terminus was appreciably more | than it should have been. This excess was equal to a certain number of the silver coins used in payment with one additional penny.' But if the correct fare had been paid by every passenger j who joined the train at this small sta- | tion the sum received by the guard ! would have amounted to one pepny i less than a whole number of pounds. The problem is to find how many passengers joined the train at this station and what was the money they paid,. ARMCHAIR PROBLEMS A woman had an ornamental clock of which the dial was of fine porcelain, but it fell down and this dial was broken into three pieces. The numbers of the hours on these three pieces when added together made three totals which were consecutive numbers. How did this arrangement happen? A rather more difficult problem is offered by tho sister of the woman mentioned above who had a similar clock which fell down, with the result that the dial was broken, into four pieces. One of these pieces was never found, but the numbers of the hours on each of the other three pieces when added together made three totals which were to one another in the ratio of two, three and thirteen. How was this arrangement brought about? LAST WEEK'S SOLUTIONS

Subscriptions to Fund.—There are 23; i persons employed in the factory. The Luncheon Table Hour.—Each man was present 11 times and absent five times. Sixteen Travellers. —It is clear that the numbers in the four boats must have been 4, 6, 6 and 7, making a total of 22, which includes the two rowers, who made three trips in addition to their own apportioned crossings. A satisfactory arrangement is that I and N were the rowers, then the parties that crossed were BIND, FINCH, JOKING, IMPANEL. Armchair Problems. —(1) A bought fivo yards at- 10s, B bought 10 yards at 9s. (2) Twopence and one farthing. (3 1 * There are three possible cases: She had four and received 59, or she had one and received 53, or she had four and received 50. The first must be rejected, because it would not have the convenience claimed for counting nines and half-dozens; the second is also inapplicable, because the words are that sho had some eggs, not ono egg. Hence the last one must be iHe correot solution. -