"NUTS!"

Evening Post, Volume CX, Issue 47, 23 August 1930, Page 14

" NUTS!"

INTELLECT SHARPENERS

All rights reserved.

(By T. Ij. Briton.)

Readers with a little ingenuity will find in this column an abundant store of entertainment, and amusement, and the solving o! 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.

IN THREE DIRECTIONS.

Here is a little problem in which a knowledge of mathematics is not necessary, but merely the exercise of some ingenuity and possibly a greater amount of 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, forty-nine in all, the initial letter of each set being different. If these be not available, take any counters at hand, marking the first sot Rl, 112, R3, etc., up to R7, and tho other letters similarly, viz., WBPYGO. The interesting problem is to place tho forty-nine 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 the 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.

LOST THEIR ROAD.

Two trampers lost their road during a tour of tho wild country, and their experience will serve as the basis of a little problem. They left the camper's hut at Deep Creek to walk to Pumice Flat, a distance of fourteen miles by direct road from their starting point, the first section being a distance of nine miles to Opua, where the road to Pumice Flat turned to the left, Opua being due east from Deep Creek. At Opua they found that two tracks turned to the left, the one running north-east and the other due north. There being no one to direct them, tho trampers took the latter track, and eventually found themselves at a place called "No Name." They learnt that the road from that point direct across country to Pumice Flat could not be travelled owing to the bridge over the unfordable Deep Creek having been washed away, that track being one mile farther than the one from Opua to "No Name." The men then retraced their steps to tho point where they had turned off, and from thence took .the north-easterly track to Pumico Flat. The question then is: how many miles did they walk unnecessarily owing to taking the wrong road?

HOW WAS IT LABELLED?

An eight-gallon keg contained thirtytwo pints of proof spirit, and another vessel with a capacity of thirty-two quarts held four gallons of distilled water. Two quarts of the spirit were poured into the keg of water, and after being thoroughly shaken half a gallon of the mixture was poured into the i keg containing tho spirituous liquor. The operator then wrote a label "Eight water to one proof spirit," which in the circumstances was correct, and affixed it to the keg holding tho mixture. He then proceeded to write one for the second vessel, but before completing it the proprietor entered the cellar, and after consultation with tho man wrote another and affixed it to the spirit keg, indicating that it contained liquor in the proportion of nine decimal two five proof spirit to one of water. AVas this correct1? If not, how should it have been labelled?

A NOVEL SQUARE. .

To add in different directions tho numbers contained in a "magic square" and find that the totals in the several ways are zero may seem to bo somewhat perplexing, but a little thought should enable tho reader to note how an arrangement of the numbers in a square will mako this possible. Looking through some correspondence on the files, from readers who devote much of their spare time to the interesting study of "magic squares," an example submitted by B.E.W. showing zero totals in this way, involves tho use of fractions, which make tho solution slightly difficult. Here is one, however, following the same principle, that does not require tho use of fractions or decimals. Take a .nino square containing that number of. digits, calling, in this ease the cipher a digit if necessary, and arrange them so that every perpendicular and every horizontal line, 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 tho bottom row is twenty.

A "SEVEN" AND AN "EIGHT."

A correspondent has forwarded a littlo problem of his own, and asks for the solution of it. It has not infrequently been pointed but that solutions are only given of problems appearing in this column, except in rare instances, owing to the large number of requests of this character received from readers, which require more time than can be spared to satisfactorily deal with. 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: "If 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 per medium of the tap, and the only other vessel available is an eight-quart 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. Picture Cards.—L 80, A 70, D 60, and S 50. The Gentleman's Dog.—Sixteen miles per hour. Two Drowned Sheep.—Kenny's pro rata share of the drover's feo being £2 ho 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 is 180 miles under tho stated conditions of tho problem. Measuring the Depth.—Fivo feet seven and a half inches. ANSWERS TO CORRESPONDENTS. "P.O."—Only when the denominator equals the sum of tho two numerators. "Driped."—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. It will be comparatively inexpensive and will be advertised in duo course, but application may be made now (without remittance), as the supply will be limited. "L0c0.," Taiiape.—The solution as published is the only correct one as you have now seen. Read standards two and four, not standards two and three. Tho transposition was obvious. Correspondence should be addressed to P.O. Box 1023.