INTELLECT SHARPENERS

Otago Daily Times, Issue 23499, 13 May 1938, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C. J. Wherefore

Correspondence should be addressed to Box 1177. Wellington.

A HALT FOR REFRESHMENTS A car stopped at a small shop which sells fruit and confectionery, and one of the passengers got out to buy some light refreshments to make the time pass more pleasantly on the journey. She found she could obtain apples at 5 for 3d and pears at 4 for 3d, while the cakes in the window were marked simply at one penny each. She spent Is Bd, and bought 30 of the commodities mentioned. All three descriptions of these were divided in equal shares among all those in the car, including the purchaser. How many persons were there? THE FAMILY SILVER “My aunt left her silver to my two sisters and myself,” said Alba. “ We were allowed to select whichever articles we fancied, and the executors did not tell us the values of any one piece, until we had quite made up our minds. If my own share had been one-third more than its assessed value, it would have been equal to that which Blanche took. If it had been worth only three-quarters of what they put on it, it would have been of value equal to Candida’s selections.” < I asked how much the entire quantity of the silver had been worth, but I was informed that that was the problem my kind friend was proposing to set for me. “ Not one of us got less than £SO worth,” she added. “There were no fractions of pounds in the estimated values, and when these were written down, we noticed that there was not an 8 anywhere on the paper.” What is the answer to my friend’s question? RAILWAY FARES -AND EXCESS When the guard entered one of the carriages of a train, which had not reached its destination until nearly 2 a.m., he found three passengers who had fallen asleep, and by doing so had passed the stations at which they intended to alight. He called upon them to pay the excess which they owed on their tickets, and the first one, A, was liable for one-sixth of the fare he had originally paid. The second one, B, had paid twopence more than A, and he was liable for only oneeighth of the cost of his ticket. C had paid one penny more than B, but he was in a hurry, and simply gave the guard one small coin before hastening away. The result was that all three men paid to the department the same amounts of money/ What were the amounts charged for their tickets, and how much excess did each man pay? ARMCHAIR PROBLEM Tom held up both hands closed, and informed those who were good enough to listen that he had some pennies in each of them. “If I had four times as many pennies in my right hand, and six times as many in my left, I should be just as well off as if I had seven times as many in my right and twice as many in my left. Which hand holds the larger number? SUBSTITUTION PROBLEM Mr Brown received a letter enclosing a cheque for a number of pounds and shillings, but without pence. For the - purpose of the problem the amount may be written thus, £A BC He happened to glance at his clock at that moment and saw that the time was A hours BC minutes, but what struck him as remarkable was that the sum of money, when expressed in shillings, makes a perfect square. Exactly twenty minutes after that he signed a letter acknowledging the receipt of the cheque. What struck him. on this occasion was that the time shown by his clock, when reduced to minutes, makes another perfect square. What was the' amount, of money, and at what time did he receive it?A MOTORING PROBLEM “ Do you want a hard problem? ” asked the professor. I replied that I should prefer a moderately difficult one to begin with, and he went on. “A few days ago I intended to drive to the house of my friend, Dr Doolittle, which is well over 60 miles away. On the road I met him coming to see me. and the product of the numbers of miles each of us had travelled is 155 times the sum of our two journeys that morning.” He seemed to be on the point of adding something, but I took my leave of him, and we did not meet again until yesterday, when he demanded that I should name the two distances which he and his friend had driven when they met. I had to confess that I wanted One more piece of information to make my solution complete, and his reply was: “ Ah, yes, that was what 1 was going to tell you when you ran away.” What is the answer I cair give, and what information should 1 have accepted when it was offered? SOLUTIONS OF LAST-WEEK’S , PROBLEMS Travellers.—The fare paid was 6s Bd. Professor’s Problem.—At the first hotel the pairs of rooms were 6,7, and 8, 9. At the second one' they were 16, 17, and 18, 19. Cattle. —J had 22 in the mob and 5 missing. B had 14 in the mob and 2 elsewhere, and R had 64. all of which were in. the yard. Armchair Problem.—There is only one arrangement which shows the same figure in all three totals, that is, • 28, 20, 52. The highest common factor. 4. is the number sold for sixpence. Book-keeping.—The clue is that the difference between B’s fifth and sixth entries must be lid. and this is the price paid by each passenger, The rest is easy—T carried 24 persons before T relieved him.