NUTS TO CRACK

Otago Witness, Issue 3961, 11 February 1930, Page 64

NUTS TO CRACK

By

T. L. Briton.

(For thr Otago Witnms.)

Readers with a little ingenuity will find in this column an abundant store ot entertainment and amusement. and the solving ot the problems should provide excellent mental exhilaration While some of the “ nuts " may appear harder than others, it will be found that none will require a sledge-hammer to crack them

Solutions will appear in our next issue, together with some tresh " nuts.”

Readers are requested not to send in their rolutions, unless these are specially asked for. but to keep them for comparison with those published in the issue following the publication ot the problems. LEVEL STAKES. Jones and Brown sat down to play a series of four games of cribbage, and had a financial interest in the results of one shilling on each game. Each started with four shillings, playing at level stakes as indicated, and each won two games, which left them both in the same position financially as they were before commencing. The next evening they played another round of four games winning two each as before. The stakes again were level on each game, but a different sum was speculated on each, with the result that Jones lost one shilling and nine pence to Brown. This curious position was not brought about by trick, as everything in the transaction was ethically correct, and this seemingly paradoxical situation may give the reader something to ponder over, for the question how one player could win one shilling and nine pence from the other when stakes are level and the number of games won and lost equal may require a good deal of thought to answer. Can the reader explain the arithmetic of it, for it is a matter of pure mathematics?

IN LIQUIDATION. A firm importing foreign-made goods recently went into liquidation, as a result, it is said, of the activities of the Buy-New-Zealand-made-goods League. The figures published provide ample data upon which to base a useful trading calculation, which, though not difficult, may serve as a brain stimulant to those who tackle it. There were two principals, X and Y, the sum that the former invested in the concern when commencing business three years ago was at the rate of £6O for 'every £4O put in by Y. At the end of the first year each partner increased his capital by 3J per cent., and at the end of the second year by 5 per cent. At the end of the third year they decided to liquidate their assets anil the question is how much did each partner invest in the enterprise originally, if he received 10s in the £ on his capital. The total assets realised £16,663 10s. Ihe statement concerning the increase of capital should be carefully noted. A PURCHASE OF EGGS. A grocer made a purchase of 525 dozens of eggs contained in 21 cases, all of equal capacity—viz.. 50 dozen—but the auctioneer, although guaranteeing the full number of eggs as given, could not state definitely 7 how many were in the respective boxes, which were all nailed down. Let us assume, then, that one-third of the boxes (marked “A”) were quite full, that half of the remain der (marked “B”) each contained exactly 7 one-half of what an “A ” box held, whilst the remaining eases (marked “C”) contained no eggs whatever. It was desired by 7 the grocer that each of his three branch stores should receive seven boxes just as they stood, so that all the shops would have an equal num her of eggs as well as cases, without any of the latter being opened. Now there is more than one way in which this could lie done, but if a stipulation is added that no shop was to receive more than three boxes of one kind—viz

“A,” “ B,” or “C”—the problem will be limited to one solution. Can the reader determine how the boxes should be apportioned?

A COMPETITIVE MOTOR RUN. A motor “ run ” was recently arranged by an automobile club, the whole 14 of tlie competitors completing the course The records to hand provide abundance of material for useful speed problems, but with all the cars they would be some what too intricate, so let us take only two of the number, which should 1 t the reader's thinking power somewhat One of these cars, “ X,” started off at 6 o'clock in the morning. It ran 30 miles the first hour, but fell off afterwards four miles hourly. At 10 o’clock car “ Y ” started from the same place, travelling along the same route, and covered 50 miles in the first hour, but, as in the case of “ X,” it too fell off afterwards by four miles hourly. Now, if both drivers agreed before starting to halt at the 150-mile post from the start until all the cars had assembled there, can the reader say whether “ Y ” overtook “X” before arrival at the halting point, and if so, where and at what time? It is assumed, of course, that the speed rates mentioned were unaltered throughout. A CRICKETER’S RECORD. A local cricketer playing in First Grade matches had the best bowling average of his team, and although his

batting average was low his all round efficiency, including fielding, enabled him to represent his province. Here are two armchair problems on some of bis figures. Up to the end of the year he had played 14 consecutive innings, in the last of which he obtained 28 runs, which increased his batting average by one run. Wliat was his average at the end of the year, there being no “ not outs?” In that year up to the completion of 13 innings by the opposing side his bowling average was 12 runs per wicket. In the fourteenth innings he secured four wickets for eight runs on a sun-crack-ing pitch, but excellent as it was, hia average was only enhanced by 7 one point by his last performance. How many wickets had he taken before getting hiq four for eight? LAST WEEK’S SOLUTIONS. A READER’S DILEMMA. Twenty-four miles per hour going out and 16 miles per hour back do not make an average of 20 miles per hour for the entire journey but 19.2 only, and that is where “C. L.” made hia mistake. The difference in time of 25 minutes is therefore correct. A QUESTION OF FENCING. As the block given up was 25 chains square it would cost £9O to fence it. The other two blocks were 15 chains square and 15 chains by 7 25 chains. THREE POULTRY FANCIERS. Jones 46, Smith 94, Brown 129: total. 269. ’ WATER, WINE AND WHISKY. Eight gallons of wine and four gallons of whisky. DULEEPSINHJI AND CONFRERES. Alex 10s in half-crowns, 8s in florins, Is in sixpences; Bruce 5s in halfcrowns, 8s in florins, 2s in shillings and Is in sixpences; Cecil 4s in florins, 4s in shillings and 2s in sixpences; each starting with ten coins totalling different sums. TWO TOUGH NUTS. A correspondent has forwarded two charades which he designates ’’ Two Tough Nuts,” and asks that their solutions be published in this colu_.n. After the bestowal of a considerable amount of time and thought in : n endeavour to elucidate their mystery, ho only point concerning them that is so far obvious is the apt name by which the correspondent has labelled them. There are therefore submitted for the mental delectation of the reader, who is invited to forward possible solutions or any 7 comments he may desire to make upon these somewhat profound No. 1. Formed long ago yet made to-day, I’m most in use whilst others sleep. What few would wish to give away And fewer still would wis l to keep. No. 2. Man cannot live without my first, Dy night and day it's used. My second is by all accursed By night ano day abused. My whole is never seen by day And never used by light. It's liked by friends when far away 7 And hated when in sight. ANSWERS TO CORRESPONDENTS. A.R.C. —“ Equate* time ” is a commercial term used in banking which means an agreed due date for one payment of a number of bills for various amounts falling due at various times. I * Weather.”—Difficult to give it on your figures .but an inch deep over an area of one acre would weigh 100 tons approx. “ Wai mate.” —Look up issues of December 28 and January 4.