INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20402, 2 November 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

A WHALE-CHASER'S MAST.

BI tl. BUXTON".

Two things likely to "strike" the eye of a visitor to the ' whaling-ship Kosmoa and the chasers, is the levelness of the former's deck and the vertical position of the latter's masts. Let us assume that the chaser's decks are also perfectly level, and that one of these vertical masts has a 52ft. rigid stay running from a point 2ft. from its top and fixed to a ringbolt ou the forward deck, and another similar stay 80ft. in length, fixed at the same spot on the mast, being also secured to a ringbolt on the after deck. It is assumed for problem purposes that the chaser's deck rum the whole length of tha vessel, and a3 stated, is perfectly level, and also that the lengths of the stays given are from the fixed point on tha mast to the deck, ignoring the diameters of the ringbolts, which are exactly 84ft. apart. Can the reader say what is tha height of the mast from the deck! This will be found to involve a useful yet very simple calculation. HIS WEEKLY WAGE. In the early spring a poultry-farmer bad an output- of 320 dozen eggs a week, the average market price during that period being 2s a dozen. Among other help, he | engaged a man at- a fixed weekly wage, but when the price of eggs went down to Ist 3d a dozen in the summer, with less than 25 per cent, increase-in the output, it was agreed that the man's remuneration should be 10 per cent, of the output at the price received bv the farmer. This arrangement was all right from the employer's standpoint, but when Easter eggs fetched about double the price, the prospects for him were not so bright. Assuming that in the week prior .to Easter the price was higher than at any period of the season, and ,that after deducting 10 per cent, of the output, the farmer had 252 dozen for himself, the man receiving £1 more by selling his quota at market price than his first fixed »%kly wage, what was the wage of the man when first engaged ? Unless very careful, the reader may ba caught with this question. A SNAIL'S CLIMB. Reversing the conditions of the old problem of a snail climbing the wall, the question requiring to be answered here is not, what was the time occupied by tha spiral-shell mollusc in reaching-the top, but how high was the wall,, and also a contingent query. When first seen tha snaiil was exactly 15in. from the ground, heading straight for the top, climbing and slipping back alternately, but maintaining a direct line. It ascended 2ft. and slipped down Ift. in alternate seconds, carrying on in this way until it reached the top, which took exactly seven seconds from the time it was first observed. What height was the wall, and where was the snail at the fifth second. The reader will get more amusement out of this problem if he solves it without pen or pencil.

SEVEN AT DINNER. Two families, one comprising the parents and one boy, the other the parents and two boys, were seated afc lunch at a round table, their positions, reading clockwise being, Grey (Gj. Simpson's wife (S.W.), Simpson (S). Harry (Hi, Charles (C), Jack (J), and Grey's wife (G.W.). It will be noted that both Grey and Simpson each bad his own wife as his right-hand neighbour. At the following two meals, however, no one was to baye the same person sitting beside him or her, an arrangement that was quite easy to make, bat as Grey occupied the same seat, at each of the three meais, and desired that Simpson's wife should sit as close as possible to him at the next two meals, but observing the "stipulation set out, and also that his own wife should occupy a seat as • far from him as those conditions would allow, can the reader arrange the sittings at the two subsequent meals, so that no one had the same person as his immediate neighbour on more than one occasion ? . A SIMPLE ALLOCATION. A man had a sum of money in bis pocket all :in silver, the amount bejng less than £l. It ■ was one of those days on which the City Council permits street, collections in support of the funds of a deserving object, and on the way to his office lie encountered three holders of nroney-bcxes. To the first collector he gave "exactly half of the amount he had, and at the same time bought an article costing threepence. In the second box he again gave half the sum he had, and at the same time bought a buttoc-Liole of violets for sixpence. The third collector had her stand just outside tne Post Office,, apd as he passed in to buy some stamps he again, placed in the box exactly half the mory?v he had left. If the final transaction was the purchase of nine penny stamps, aftr/r which he had only threepence left, ran the reader calculate how much the .man had in his pocket at first ? LAST WEEK'S SOLUTIONS. Good Handicapping. If Y gave Z a start of 25ft. in a race of 1.50 yards, both leaving their marks together, the result would be a " dfi<4lieatrunning at the relative speeds stated. A Strange Number. The number is 12545679, and the demonstrator's multiplier always nine. Two Cash - Dockets. The dockets showed Is and Is the woman having no coins of a higher denomination than Is. Within a Triangular Field. The outer circumference of the track is approximately 29 yards more than the length of the inner circumference. Catching a Train. The car set down the first pair after travelling 12 miles, and returning picked up the other two who had walked four miles. everyone reached the station together, 1 hour and 56 minutes after starting. ANSWERS TO CORRESPONDENTS. G.C.A.—It is a fallacy that often puzzles some people until explained by demonstration. " Inquirer."—Every game should be drawn if both play correctly. Id the ancient game of " noughts and crosses" a person who knows, can win every game against a player * not understanding the correct method, and it does not matter whether he commences or not.