INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20626, 26 July 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

WATCH THAT STOPPED.

BY T. L. BItITON

A motor fatality was that of a man who was driving by himself, and afterward found dead upon the road by his wrecked car, which had collided with a lorry. Ilis watch was stopped by the impact, both hands being together. The man was seen a few minutes after midnight, driving along the road, his body being discovered at 2 a.m. With thesa particulars and the fact that the medical testimony was to the effect that death was instantaneous, resulting from the same blow as which stopped the watch, can the reader determine the exact time that the accident occurred.

A COUNTRY SCHOOL. At a certain country school there were only five standards. lhe number in Standard I. was one fewer than a third of the enrolment of Standard I\., and three fewer than half tho number in Standard Y. 'I hose in Standards .11. and Jli. outnumbered the total of those in Standards 111. and V. by tlnce, and tho pupils in Standard 111, together with Standard IV. totalled one fewer than half the number in the five standards combined. As the number in Standards 111. and V. together equalled seven-sixteenths of the school's total enrolment, one of these two containing one quarter of the whole total, can the reader say how many pupils were enrolled in tho five standards respectively ?

TWO CYCLISTS

Jones and .Jenkins were cycling, th«ir destination being a stock camping reserve, " X." They were not riding together, Jones being a considerable distance .ahead of his mate, though both were riding at the same speed. At the fiftieth miie post from " X," Jones overtook a (lock of sheep which travelled at the rate of three miles in two hour:.;, and two hours afterward he met a rnob of cattle moving along at the rate of nine mile 3 in four hours. Jenkins overtook the sheep at the fortyfifth mile post from " X," and met the cattle at exactly forty minutes before he came to the thirty-fust mile post. It is quite easy to find from these details how far Jenkins was from " X" when Jones arrived there. Can the reader calculate this ?

SIMPLER THAN IT MAY LOOK

If a coin be laid on a table, six others of the same size can be placed around it, so that all of them touch the central coin. Exactly the same thing applies to solid spheres, and this fact prompts a problem which is much easier than it may look. It does not concern ratios of diameters and radii to circles or solid spheres, a knowledge of elementary arithemetic being all that is necessary to enable the solver to quickly find the correct answer. Six solid spheres are placed around a central one, in the manner indicated. Then if it be granted that the area of the surface of each of them is as many square inches as there are cubic, inches in its volume, what is the length of the diameter? When giving the solution next Saturday, the method of arriving at it will be explained.

SOVEREIGNS IN BAGS.

Weighing soveriegns instead of counting them is obviously a quicker process their correct number, when the quantity is a large one, but the placing of the coins in s? iled bags, each containing a fixed number, simplifies very c msiderably, the work of paying out. Hero is a question which, as often as not, puzzles for a while, the person who tackles it, though a little thought wiil enable the simplicity of the question to be quickly seen. A certain sum in sovereigns is contained in eight bags, each of which holds a different number of coins, and any amount from £1 (one) to £2OO (two hundred), can be paid by handing over one or more bags without opening them, and not giving more than one bag containing the same number of sovereigns. How many sovereigns should be placed in each bag to enable this to be d< ie, a different sum being in each 1

LAST WEEK'S SOLUTIONS

Transposing a Figure.—'The number is 142557. Bv transposing the last figure to tho beginning, it reads 714235, which after placing a decimal point between tho last two figures, 's a correct division of fliporiginal number by two.

Miss Putter and Miss Green.—The former started with 7s and Miss Green with 3s 6d, the latter winning 2s 4d. Blending o! Teas.—Twelve pounds _*t 3s 4d. three-quarters of a pound at 3s, and two and a quarter pounds at 2s 4d per lb.

Two Circus Rings. —Twenty-five feet from tho tent-pole to the circumference of tho larger ring. It was assumed that neither had any geometrical breadth, In a Quadrangle.—The height is six feet, the width of the quadrangle not being material. Formula: —The product of the two heights divided by their sum.

ANSWERS TO CORRESPONDENTS

X.—Yes, a fallacy, but hardly a para do.v.

" Euclid."—64o acres, whether it is a square mile or a miie square.

" Dispute."—Windermere is the largest lake in England, but is a " pond " in comparison with Taupo, being hardly six square miles in area, and not a mile across at its widest part.