INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20650, 23 August 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

IN THREE DIRECTIONS^

BY X. L. BRITON. Here is ''a problem in which "a know* ledge of mathematics is not necessary, but merely the exercise of some ingenuity, and possibly, greater patience. Take seven counters of any colour or distinguishing mark, say for example, red,and a similar number of each of six other colours, white, blue, pink, yellow, green and orange, 49 in all, the initial letter of each set being different. If these be not available take any counters at hand, marking tho first set El, R2, R3, etc., up to R7, and the other letters similarly, "viz.: W, B^-J 5 , Y, G, 0. The interesting problem is to place the 49 on a board of that number of Squares so that no letter and no number shall appear more than once in any diagonal, horizontal or perpendicular line. By. " diagonal" is meant tho two long diagonals and also the shorter ones which run parallel to them. A half-hour should quickly pass while so employed, and quite possibly before the feat has been accomplished. THE WRONG- ROAD. Two trampers lost their road during a tour of wild country. They left a camper's hut at Deep Creek to walk to Pumice Flat, a distance of 14 miles by direct road, from their starting point, the first section being a distance of nino miles to Opua, where tho road to Pumice Flat turned to the left, Opua being duo east from Deep Creek. At Qpua, they found that two tracks turned' to tho left, tho one running north-east and the other due north. There being no one to direct them, the trampers took the latter track, and eventually found themselves at a place called No Name. They learnt that tho road from that point, direct across country to Pumico Flat, could not bo travelled owing to the bridge over the unfordable Deep Creek having been washed away, that track being one mile farther than tho one from Opua to No Name. The men then retraced their steps to the point where they had turned off, and from thence took the north-easterly track to Pumice Flat. How many miles did they walk unnecessarily owing to taking the wrong r<|id ?

A MATTER OF LABELS. An eight-gallon keg, containing 32 pints of proof spirit, and another vessel with a capacity of 32 quarts, held four gallons of distilled water.. Two quarts of the spirit were poured into the keg of water, and after being thoroughly shaken, a half gallon of the mixture was poured into the keg containing the spiritous liquor. The operator then wrote a. label " Eight water to one proof spirit," which in tne circumstances was correct, and affixed it to the keg holding the mixture. Ho then proceeded to write one for the second vessel, but before completing it,the proprietor entered the cellar, and after consulting with the man wrote another and affixed it to the spirit-keg, indicating that it contained liquor in the proportion of 9.25 proof spirit, to one of water. Was this correct; if not, how should it have been labelled? A NOVEL SQUARE. , To add in different directions, the numbers contained in a " magic square," and find the totals in the several ways are zero, may seem to be somewhat perplexing, but a little thought should enable the reader to note how an arrangement' of the numbers in a square will make this possible. Looking through sortie correspondence from readers who devote much of their spare time to the interesting study of " magic squares," an example submitted by 8.E.W., Bhowing zero totals in this way, involves the use of fractions, which make the solution slightly difficult. Here is one, however, following the same principle, that does not require the use of fractions or decimals. Take a nine square, containing that number of digits, calling in this case, the cipher a digit if necessary, and arrange them so that every perpendicular and eveiy horizontal lino, as well as the long diagonals, will total zero. They should be in such positions that the sum of the first and third figures in the top line, the third in the middle row, and the middle figure in the bottom row is,2o. "SEVEN" AND AN «EIGHT." A correspondent has forwarded a problem of his own, and asks for the solution. It has not infrequently been pointed out that the solutions are given only of problems appearing in this column except in rare instances, owing to the large number of requests of this character received from which require more time than can be spared to satisfactorily deal with them. In the present case, however, the problem submitted by the correspondent may well find a place in this column, as it involves a useful and every-day calculation, though rather simple. He writes:—"lf a person with a seven-quart vessel desires four quarts of the contents of a large and fixed milk container, from which the milk is only obtainable by means of the tap, and the only other vessel available is an eightquart can, what is the fewest number of operations necessary to achieve his purpose, an operation being one pouring from either of the two vessels ?" Can the reader enlighten him ? LAST WEEK'S SOLUTIONS./ Cigarette Picture Cards.—L., 80; A., 70; D., 60; and S., 50. Man and a Dog.—Sixteen miles per hour. Two Drowned Sheep.—Kenny's pro rata share of the drover's fee being £2, he owed Lucas 30s, and also 9s as his proportionate share of the dead sheep, while Lucas was indebted to him 9s 4d, being two-thirds of the value of the two skins. Two Ferry Steamers.—The distance ia 180 miles under the stated conditions of the problem. Depth of a Pond. —Five feet, seven and a-half inches. ANSWERS TO CORRESPONDENTS. P.O.—Only when the denominator equals the sum of the two numerators. " Drl-ped."—lt is intended to publish a selection of the most interesting of the problems, together with a number of useful formulae and rules not generally to be found in text books; they will be comparatively inexpensive. It will be advertised in duo course, but application may bo made now, (without remittance), as the supply will be limited. " Loco." Taihape,—The Solution as published is the only correct one as you have now seen. Read standards two and four, not standards two and three, the transposition being obvious.