INTELLECT SHARPENERS

Otago Daily Times, Issue 20075, 16 April 1927, Page 21

INTELLECT SHARPENERS

By T. L. Barrow. Reader* with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of the problem* 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 it. Readers are requested not to sena in their solutions, unless these are . specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. SHUNTING. Shunting problems seem to find favour in many publications abroad, and they still comprise many of the hardest ‘‘nuts'’ in railway examination papers. As several readers have suggested an occasional problem of this character, here is one, which, though not very difficult, will still require some thinking to solve it under its prescribed conditions. A loop line branches olf the mam track at A and rejoins at B, a distance of about SO chains. About half-way along the loop is an overhead bridge, under which carriages, out not the engine, can pass. On one side is a carriage X, and on the other side of the bridge stands another, Y, the engine being on the main line. The problem is to use the engine as in ordinary shunting operations, and change X to the position of Y and vice-versa. Can the reader do this theoretically in four operations, each contact of engine to coach counting as one, and leaving the engine on the main line? A MUTILATED HEARTH RUG. A lady friend had been brushing and cleaning her fur coat, using prepared soap and water. The day being wet she hung the coat in front of the ure to dry, but during her absence from the room it fell, and before the mishap was discovered, it was irretrievably burnt, as well as portion of the hearth rug. As the coat was partially covered by insurance, my friend was more concerned about the pretty rug which was not her property. The size of the rug was three feet by two feet three inches, and upon examination it was found that two diagonal corners had been completely destroyed. When told about the accident the landlady took the matter very generously, and decided to cut oS the burnt parts from a point six inches from the corner on the longer side to a point 12 inches from the same corner on the shorter side The same procedure was followed at the other corner The rug was then in the form of* a hexagon (six sides), and the owner desires to know whether it can be made into a square piece without further waste, and without cutting the rug into more than two pieces Can the reader tell her? A BOY’S BALANCE. A little boy being allowed to remain from school one day found that the absence of any playmates made the time pass very slowly. Playing by himself on a see-saw made this more apparent, for without somebody or * something at the other end of it there was not much fun, he thought. But he was qn ingenious little chap, and, seeing some bricks nearby, he tied a number on. one end getting the exact balance for his weight; and for a time no see-saw ever worked better, for though one end was longer than the other, the plank was secured by a fixed pivot- The boy played for a while, and then thought that the topical expression of “change over’’ might apply in his case, so he tied the bricKS at the other end of the plank. But it did not work so well, for he found that though eight bricks were enough at first, 18 were now necessary to properly balance his weight As each brick weighed two pounds and a half and half a brick, what was the boy’s weight ? THIRTY-FOUR LINKS. A chain ; 18 inches long, consisting of 34 links, ‘ had been broken into seven pieces, the largest containing six links and the smallest three. The owner of it desired to have the fragments rejoined, and to make the chain the same length as before, none of the links having been lost It cost twopence to open a link and fourpence to wold, and a new chain of the same kind would cost two shillings and ninepence. What was the most economical course to follow —to purchase a new chain or have the old one repaired, the assumption being that, once mended, the chain would be as good as new ? LAYING EGGS. A correspondent has sent me a problem m an apparently complicated form on the ancient subject of egg-laying, but as it is somewhat different from the usual, and is quite new (to me), it is offered to the reader for his serious consideration. My correspondent has omitted to send any solution, and it may be risky to publish the problem in anticipation of receiving it, as no problem must appear in this column that is not capable of being solved. But to make sure of a solution of it ap pearing next Saturday I shall apportion the necessary time during the week to find one, should’my friend disappoint. Here is the problem : If a hen and a half lay an egg and a half in a day and a half, how many and a half which lay better by a half will lay half a score and a half in a week and a half? LAST WEEK’S SOLUTIONS. A SUBURBAN TENNIS GROUNDThe gentleman must have given fifty rails 12 feet long, of which 49 were used enclosing half an acre less 19 square yards. A TWENTY-FIVE SQUARE. There are exactly 100 solutions using each figure as the centre four times, and with this information the reader _ has enough pastime for many winter evenings. CURIOUS MULTIPLICATION. There are only seven examples of this curiosity, including the one given. The others are: 12 X 483 = 5796; 42 x 138 = 5796; 18 x 297 = 6346; 27 x 198 = 5346; 30 x 186 = 7254 ; and 23 x 157 = 4396. THE BEVERAGES. The ale must have been in the 10-gallon cask. A CARPENTER’S ECONOMY. By finding the half-way point in the right-hand side of the square and cutting a direct lino to the apex of the triangle would give one portion of the new square. Then from the same point to the lefthand bottom corner of the original square, if cut, would give three pieces of board, which, if joined properly, will make a perfect square. ANSWERS TO CORRESPONDENTS. ‘‘Figures.” —Y"es, there are only seven solutions, “T.G.” —There is no other solution, but manv imaginary ones. “j j» ” —Thaiiks for your interest, hut am afraid time will not permit of looking into these, hut if solutions are sent they will be examined.