"NUTS!"

Evening Post, Volume CVI, Issue 132, 15 December 1928, Page 30

"NUTS!"

| (By T. L. Briton.) | i IIIItMIIMHIIIIHItimii

INTELLECT SHARPENERS f | All rights reserved. |

Senders 'with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of tee problems should provide excellent mental exhilaration. While boom of the "nuts" may appear harder than other*, it will be found that none will require a sledge-hammer to crack them. A MEASUREMENT PARADOX. "Nemo writes to ask "Why is it that if a square of stated size be cut into four pieces in a BSrtain way without any waste, and those parts placed together in the form of an oblong the latter will have a greater superficial area than the original square?" Tho correspondent evidently has in mind an old paradox discovered by the mathematician Lucas, and is worth recording, as it will perhaps be new to a number of readers. A square piece of cardboard eight inches by eight is marked from a point A on the top "side three inches from the loft-hand corner by a line to C on the base, which lino is parallel to the sides. In the line AC a point is marked at D three inches from A, and on tho right side of the square a point is marked at B fivo inches from the top right-hand corner. By drawing a line from the top left-hand corner to C, and another from B to D, the square will be marked into two triangles of equal size, and two four-sided figures of the equal measurement, and if the square be cut into these four parts, the pieces can.be fitted-to: form an oblong apparently thirteen inches by five, or 65 square inches instead of 64 square inches in the original square. Can the reader enlighten "Nemo" on this paradox? THE CONSUMER PAYS. When the subject of the high cost of living is being discussed it often occurs that the middleman is given the blame and not the primary producer or the manufacturer. An illustration of this point was revealed in the Arbitration Court recently, when the following figures were produced which will give the reader an insight into a useful little calculation. The market price as between the retailer and the consumer on a certain article is three pounds six shillings—£3 6s. The manufacturer made ten per cent, upon it when selling to the storekeeper, who admitted in evidence that his profit on the article was exactly fifty per cent. In asking the reader to say what was the cost of production to the manufacturer, it should be noted that "per centago of profit" is correctly based upon "cost" and not on "selling" price, however expedient it may be to traders to calculate otherwise. AN IRREGULAR-SHAPED FIELD. When opening up some new country in. the North recently a. one-chain road was made through a privately-owned paddock, the northern part thus forming an irregular-shaped field. After that portion had been fenced it was found that the north boundary running cast and west was exactly fifteen chains in

I length, and that tho south line of twen-ty-five chains was parallel to! tho other, I hose two boundaries being thirteen I'haius apart. Tho Government paid Mio owner for tho land excised for this road (which ran along tho full length of the south boundary of the field), at Hie rate of £10 per acre, the total sum just equalling tho cost .of erecting the <'xtra fencing required, but not covering other expenses to the owner which u-ero incurred by the resumption. If, however, he made a profit from his first crop off the field of 15s an acre, by how much did ho benefit financially after paying £12 10s for "other expenses," ! and what sum was paid to him for the area excised for the road'? THE BOARD-ROOM CLOCK. j A clock in the Board-room of ,ono of the public institutions was fixed on one of the walls, these being exactly 12ft Sin high, but ,what height the clock was from the floor is not available. Some time ago the room was lengthened to 71ft 9in for the purposes of a lecturehall, the two walls thus extended including the one upon which the timepiece was fixed (though the.clock was retain,ed in its original position) the height of the-walla remaining*as before. Upon entering tho hall one. day recently it was noticed that the hands of tho clock were . pointing in diametrically oposito directions, and a curious thing about them also was that the straight line thus formed was parallel to one of the diagonals of the wall on which the clock was fixed. Can the reader say to within half a minute what time of the day it was as then indicated by this Board-room clock? WATER SCOUTS. During a recent encampment of the Boy Scouts, most of them got their greatest fun in the water, and the few flat-bottomed boats available were constantly in commission. The only difficulty was that none of the craft could hold more than three boys, and it is this fact that prompts the present problem. Let us suppose that fifteen scouts went out in the boats at the same time on every day in the week, including Sundays,; and that three boys (no more or less): manned each boat—what is the fewest number of boats that would be required if it is also stipulated that no two scouts should go together in any boat more than once, and that no one should go out twice in the same boat? To arrange the daily groups in conformity with these conditions and thus find the fewest number of boats necessary will give the reader a good measure of mental exercise. LAST WEEK'S SOLUTIONS. A Rescue Ship. —The captain was awarded £250 as prize money, each of the officers £62 10s, while the 36 men received £15 12s 6d each. The salary of each of the three officers was consequently £250 per annum. Nibbling a Hedge. —Under the conditions of the problem it was possible for the donkey to nibble the hedge for a lengtn of thirty-six feet. Another Tethered Donkey. —lf the donkey is tethered to a line 48yd Sin in length from a post in ono of the corners of the half-acre field, it will be able to feed on exactly one quarter of an acre, assuming it can graze to the end of the tether. The length given ignores a fraction of an inch. Two Incomes. —The amount drawn by Smith must have been £194 5s for the year, while Jones drew the sum of £244 14s. A Square Girder. —The profit made was 37s 6d, being made up by 80 cubic

feet of the cylindrical trunk (which measured originally 220 cubic feot) the cubical contents of the girder being therefore 140 feet. ANSWERS TO CORRESPONDENTS. "A.H.K."—See this issue. "COMPAEISON."—Yes, that was tho pitfall hinted at. "SHEEPMAN."—The number of different ways is 47. A.problem on tho point will appear later.