INTELLECT SHARPENERS

Otago Daily Times, Issue 22741, 29 November 1935, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times. By C. J. Wherefore. [Correspondence should be addressed to Box 1177, Wellington.] CHARADE. To Silver, at the blockhouse door, The captain spoko with care: " I'll take you to your SECOND shore, To stand your trial there. There's one WHOLE, it is true, That when we meet again, I'll put a bullet into you, And whatsoever I may do, I'll FIRST neither plan nor view, So that's my warning plain." MAKING A.PROFIT. A secondhand dealer had been absent from his place of business, and when he returned he found that his second-in-command had sold a bicycle. He was inclined -to find fault with his assistant for having accepted less than the price which had been placed upon it, which was a number of pounds without additional shillings and pence. The reply was: "I had to make a small allowance, but we still make quite a tolerable profit. The money received is just six times as much as we paid for it, and the allowance I gave was Is 5d less than the excess over f 1 in the original price we paid." How much had they paid for the bicycle, and at what price did Jhey eell it? ARMCHAIR PROBLEM. An entry on an invoice showed a result similar to the following, but letters are now written in place of the figures:— MN yards at A shillings, B pence per yard—fC Cs Cd. The numbers of shillings and pence, A and B, when added together make 11, and the two numerals M and N which form the number of yards also make .11 when added together. What are the numerical values of M and N? A BILL FOR REPAIRS. "We stopped for lunch at rather an expensive place," said Mr Motorist. "After settling for this at the hotel we were very short of cash, and when we found it necessary to pay for a repair, fortunately a very small one, all five of us had to turn out our pockets. Even then there was a small deficiency, which I shall have to send by post. I paid two-fifths of the amount and my wife paid one-fifth. My daughter paid threetenths, and my two small sons 'onetwentieth and one-thirtieth. The numbers of pence which the two boys paid, when . multiplied together, make just half the number of pence which their sister contributed. So now, of course, you can easily discover how much we all paid." PIGS IN CLOVER. The following is a reduction to presentday standards of intellect of a problem which used to delight the minds of our grandfathers and other primitive folk:— A farmer put some pigs into four different paddocks. Into paddock No. 2 he put twice as many as into No. 1, into No. 3 he put twice as many as into No. 2, and into No. 4 he put twice as many as into No. 3. A thief came along, with a motor lorry probably, intending for reasons of his own to steal the same number out of each of the paddocks, but he could not do so until he had driven a few pigs from No. 4 into No. 1. Then he carried out his original plan of taking equal numbers from each paddock, and that left exactly 100 pigs behind. Ho\y many pigs were there, how many did he find necessary to transfer from one paddock to another, and how many did he steal from each paddock after making this adjustment? THE TRAMPING CLUB AGAIN. " Can you help me with another problem, Miss Remington? " "Do you think you deserve one ? " she replied. " You were not a model of politeness aboutone I gave you before; you said it was capable of several solutions. Very well, if you promise you won't do it again, I'll tell you about another exploit of our Tramping Club. We had an invitation from Mr Banksia to visit his gardens, and his flowers were worth seeing and remembering, in case you may have the idea that you know anything about such unproblematical things. But then he took us to a tea shop just alongside, and we had a tea that was worth seeing and remembering also. He told me he was paying a fixed price per head, and, although he did not mention what it was, he hinted that he hoped we should take care to get our value. And then a queer thing happened. He handed the girl a £5 note, and she had no change, so he gave her several £1 notes instead, and it was one penny too little. He had no pennies, so I suppose they had to book this deficit against him. Now, how many of us were there, and what was the price charged? " I remembered just in time what I was pledged not to say, so I restrained myself and asked how they had arranged themselves in the matter of seating. "We sat at tables for four persons, except Mr Banksia, who had a table all by himself. Now can you find one solitary satisfying solution?" It was clear that she had not failed to see how near I had been to repeating my transgression. I assured her that I knew the answer. What is it? SOLUTIONS OF LAST WEEK'S PROBLEMS. gheep.—lsl2, 864, and 648 acres. Books. —The ages were 28, 7, and 5 years, and the books cost 14s, 3s 6d, and 2s 6d. Driving and Walking.—The cars were driven at 36 and 12 miles per hour, but the interesting point is that the distance can not be known, because the results described would be true with any distance we may choose. Error in addition.—The error must bave been threepence, because *.he amounts mentioned would add up to £1 Os 3d. With reference to the individual sums, the systematic arrangement would probably be: Is Od, 2s 3d, 4s 7d, 5s Bd, 63 9d. But there are more than 100 ways of making the total given above, so that it is not possible to find a sure answer to this part of the problem. Armchair Problems.—(l) The only difficulty is that, there seem to be so many solutions. But it is clear that B had the smallest number, and this was an odd number exceeding 10, so that it was evidently 11. Therefore A had 28 and C had 40, before he lost 23 of them, as described. (2) This cannot be solved without taking the stamps into account, but it is obvious that there were two which cost one penny each. The books cost half a crown and eighteen pence.