INTELLECT SHARPENERS.

New Zealand Herald, Volume LXIV, Issue 19608, 9 April 1927, Page 5 (Supplement)

INTELLECT SHARPENERS.

Br x. z. bhitont Readers with a little ingenuity will find in this column an abundant stoiif of entertainment and amusement, and the solving of the problems thould provide excellent mental exhilaration. While some of the " nuts '* may appear harder than others, it will be found that nona will require &. sledge hammer to crack it. Readers are requested not to send in their solutions unless specially asked for, but to keep them for comparison with those 'which will appear each Saturday, following the publication of the problems. SUBURBAN" TENNIS GROUND. It is generally agreed that there is a practical usefulness in problems. A suburban property owner was asked by a deputation of young ladies for the use of some ground for tennis purposes. " What area would you require," li.e asked, and was told about half an acre, sufficient for two courts, a shelter shed and seating accommodation. Taking out pencil and paper, he made some rough calculations, and replied. " There are a number of dressed rails on some vacant land nearby, just five less than the ten chains in total length. You may use them as top rails only, and may fence in as much land as they will enclose, provided it be in the form of a perfecti square." When the land was fenced in this way there was one rail enclosure being exactly 19 square yards lesa than half an acre. As nothing was lost in the length of any of the rails used, how many did the owner give to the deputation ? A TWENTY-FIVE SQUARE. The square given* below consists of the numbers 1 to 25 arranged so that there are 40 different combinations of five numbers—in systematic arrangement and not irregular groups—totalling 65. There are several ways that the figures may be placed in the form of a square which will give the same result. How many arrangements can the reader discover? - - - • 8 21 14 2 20 4 17 10 23 11 25 13 1 19 7 16 9 22 15 3 12 5 18 6 24 CURIOUS MULTIPLICATION. Therp are only a few examples of the following peculiarities in multiplication, and although not difficult to discover, the ' effort to find them gives much amusement, and entails quite a lot of interesting calculation. The problem is to find, a number consisting of two figures only, and multiply it by another s number of three figures, all different from the first* mentioned, so that the product, consists of the remaining four figures of the nine digits. The whole nine figures are thus contained in the problem, but no figure* appears twice. Here is an example:—■ Multiply 48 by 159 and the result is 7632, thus each digit, 1, 2, 3, 4, 5, 6/ 7, 8, 9, is used once only. There are .six other examples, and if the reader can" discover them in one evening's effort, he .will finji that his intellect has been sharpened' materially. a —_« . -Ef -7 THE BEVERAGES, j A wholesale manufacturer of gingerbeer had in his cellar, on one occasion, a ' cask of ale for his own consumption. The brewery, however, required the cask, so the ale was placed in an empty gingerbees- barrel. These were all similar in construction but of varying sizes, and at. this time there were six barrels in the cellar, five of which contained ginger-beer, the other the ale. In outward appearance they were the same in all but Size, the only marks on them being, 10. and 15£, indicating the number of gallons each barrel held. Two coders ; for ginger-beer had just come in, j one for exactly twice the quantity as the, other, and the manufacturer found that he could suDoly these orders without interfering with the barrels or contents in any wav, and without the customers bei]ng any wiser as to what one of them contained. "From these facts can the reader determine which barrel held- the ale ? x A CARPENTER'S ECONOMY. A carpenter had a piece of rimu of the exact superficial measurement that he required for a square table-tcp, but it was of irregular shape, requiring cutting and ' joining together. The lower part of it was perfectly square, and the top in the form of a gable (isoscles triangle),, its base being the top side of the - square. The board had been cut in this shape;- by a tradesman, so all sides were quite, thie, and the size of the'square was exactly four times that of the triangular portion. The carpenter's problem was to fins! how the board should be cut, so that there would be no waste whatever, and the pieces capable of being joined to form, a perfectly snuare board. Can the , reader advise him ? \ ■ ■ M;i't LAST WEEK'S SOLUTIONS. After Many Counts. There must have been 301 eggs, as number (being less than 40 dozen), ifdivided by 2, 3, 4, 5, 6, 10 or 12, will leave one over in each case. There was* therefore, one over when the wife counted them. The Snail. The correct answer is eight days andti nine nights. Loyd's curious solution wa3 that he reached the top on the tenth night. Country Cricket. K—'s two innings were 100 and 80 rtn. spectively, and M—'s 80 and 96, thai,. former, therefore, winning by four runs* Fifteen-Sixteen Etc. If the nine cards be placed in the order! shown, they will count 15 in eight differ* ent ways, scoring as it were, " fifteen* sixteen," 438 951 276 There are upward of 10,000 different ■ways of placing the cards one to nine in the form of the letter T, so that their spots will count the same in the column as in the top line. Mixed Numbers. The solitary instance of the number 100 being capable of ' expression as a mixed number with only one figure in its integral part, and using each of the nine digits once only, is 3 69258-714. ANSWERS TO CORRESPONDENTS. C.S.D.—Yes, the solution could be obtained by trials, somewhat laborious, bu« why that way when the data are ample* G. P.—Relationship problems have prefer* ence with some, but hardly the They will appear occasionally. H.B.—H§ spent that amount in two yeara, notone* , P.T., " Cheerio."—Replies bj; post as quested.;