INTELLECT SHARPENERS.

Otago Daily Times, Issue 19981, 24 December 1926, Page 23

INTELLECT SHARPENERS.

By T. L. Briton. Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some ot the “nuts” may appear harder than others, it will be found that none will require a sledgehammer to crack them. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published in the week following the publication of the problems. A LONG WALK. Exactly one mile south from the Kurow bridge, two bush tracks branch off from the Main road, both to the right, but one more so than the other. One of these leads to a bushme.Ts camp at K—, the other to a little settlement at o—, and both tracks are perfectly straight. I set out the other morning to walk from the bridge to o—, but unfortunately took the wrong track to K —, and did not discover the mistake until I arrived at that place. I was informed 'by some men there that the nearest point from K — to the road which I should have taken, was three miles, but as there was no defined track to it, I decided to con' tinue from K— to O— by the road, which was a straight one, and exactly the same distance as I had already travelled to K—from the point where the tracks branched off. I arrived at O — some hours later than intended, and upon my tolling the schoolmaster of the route I had inadvertently taken, ho informed mo that I had walked exactly 11 miles intead of —; but probably tho reader will discover from the above, how many miles it is from the bridge to O— by the direct route. AN APPLE ORCHARD. When a land owner in the Timaru district was making a division of his properties, he erected a fence through an apple orchard, dividing it into two unequal parts, the large portion containing three times as many trees as the other. This section hq gave to his elder son, who had remained at home to help with the work on the farm, while the smaller section was given to the ether son. a somewhat prodigal young man. When the father died, the latter boy decided to uproot the trees on his portion and have the land (which was close to the township) subdivided for building sites. When the surveyor measured it. he found two curious facts—viz., that besides the elder son’s portion containing three times as many trees as the smaller section, it was exactly three times the area, and also that the difference between the size of the portions of Ihe orchard given to the sons was tho same as the difference between their squares. What was the original size of the orchard? THE BISHOP’S ANSWER. Two laymen and bishop were chatting in a golf club room a few Saturday afternoons ago, and amongst other things discussed was the evergreen one of gambling. “No,” said the bishop, “gambling in the abstract is not a sin, and where no undue advantage is usurped by one player against another, no conceivable harm can result in one benefiting financially from the other, provided the loss be well within the loser’s means. Of course,” he added, “I am referring only to games or sport demanding the exercise of skill.” “Supposing, then, your lordship, that my friend here and myself sit down to play dominoes, and he stakes half of the money he holds upon each game played.' We play 12 games, each winning six, the games, of course, being played strictly according to the rules and etiquette. Would it be correct. to say in this case that neither player had any advantage over the other?” “Undoubtedly,” replied the bishop, “particularly as neither player could have been a loser at the end of the 12 games.” Was the bishop correct in his last statement? A SOMEWHAT DIFFERENT ONE. Here is a little variation from the orthodox crossword problem. As it is entirely new, so far as I know, there can be no published solution of it. Not that it is difficult, but the fact that in composing it the beaten track has not been followed will make it perhaps more interesting to 12 3 4 5 6 7 i Horizontal: Vertical: 1. An animal. 1. Insects. 5. A mistake. 2. To put to some 6. On the Stock purpose. Exchange. 3. Measures of length. 7. An edict. 4 In “intellect.” All squares are used. ’ MARY AND ANN. The late Sam Lloyd was one of tho world’s best chess problem composers, yet he found time for puzzles of many vanities. Here is one that will require a brain absolutely clear of cobwebs to arrive at the correct solution:—The combined ages of Mary and Ann are 44 years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann. Mr R. has sent me this one, but has not sent the solution. I am, however, including it in this week's contribution, relying upon being able to solve it for publication next week. SOLUTIONS OF LAST WEEK’S PROBLEMS. THE OLD BOY. The “Old Boy” was 24 years of ago A RICH PERFUME. Tho first son received three full jars, one half-full and three empty ones; the second son, two full jars, three half-lull and two empty ones; the third son, two full jars, three half-full and two empty ones. THE TWO TYPISTS. The reader will perhaps be surprised to know that by receiving her advance in salary half-yearly, Miss Remington received in five years £l2 10s more than Miss Underwood, whose increase was paid yearly; their earnings in that time being £362 10s and £350 respectively. As the proportion of the amount of the former’s dress bills to her salary was one and a-half times that of Miss Underwood’s to her receipts, Miss Remington paid her dressmaker £217 10s (60 per cent.) and hcr_ cousin paid £l4O (40 per cent.) in the period stated; a total of £357 10s. TWO LONELY NUMBERS. The lonely numbers are 48 and 1680, each of which by adding 1 to either the whole or half, will become si square number. BLACK AND WHITE MONKEYS. Number the seven squares so that the figures are not obscured by the pieces, and the following 10 moves will achieve the desired result:—2 to 1, 5 to 2, 3 to 5, 6 to 3, 7 to 6, 4 to 7. I to 4, 3 to 1, 6 to 3, 7 to 6. THE NINE COUNTERS. This problem, published on December 4, was sent to mo by Mr K., of Nelson. Since publication I have received scores of solutions in four moves, for which I thank the solvers, and Mr K. has been notified accordingly. I am now examining this problem and hope to publish a solution in three moves.