INTELLECT SHARPENERS.

Otago Daily Times, Issue 20702, 27 April 1929, Page 21

INTELLECT SHARPENERS.

By T. L. Bbiton.

A GARDEN PATH. Here is a little problem concerning the laying down of a garden path that may interest the reader in a practical v." y as as provide a useful calculation. A plot of land, oblong in shape, 36 feet by 1,5 feet, is to be planted with carnations in a centra] bed with a concrete path running round it of such uniform width that it will occupy exactly half the area of the whole plot,* What width should the path be? Although the measurement of the plot is given in order to make an easy mathematical problem of It, there is a simple and practical method of determining the width of a path (under these conditions) of any oblong plot without requiring to know the actual dimensions of the section. Tihi s method, which is quite useful to know, will appear next Saturday; together with the solution of the problem now stated, TWO HEN AND A BOY. Two men undertook to do a certain job together for the sum of £4, agreeing that one of them could do it alone in five days, and 1 the other in eight days. But as the Easter holidays were close at hand, giving them loss than five days to carry it put., they decided before starting to obtain- the help of a boy. and the three working together started and completed the job in three days. Can the reader say to how much of the £4 the boy was entitled, on the assumption that the two men worked up to then- respective capacities as stated. Although this is an absurdly easy calculation, the question reached me from a Standard Vl pupil, who, in sending an answer (the correct one) says he cannot see how it is arrived at. A GOLF TOURNAMENT. • iff not ahvays an easy matter to construct a. plan of play for a tournament w-hen, as is often the case, the number or competitors is large and the conditions unusual. But let us take six players only m a golf tournament who are' required to be “paired” under the followmg three conditions and try to construct a table, accordingly. The reader who sikccecls in accomplishing this, in, say, a quarter of an hour, will probably find that Ins mind has been fairly active during ‘be The conditions are:— (1) Every competitor shall play every oihei% once, and only once. (2) Only three links to be used, every playqr playing twice on each of two of them- and once only on the other. . (3) Ail competitors play simultaneously in e.\ery round, and in the last one every one of the six plays on links for the first time,. r T ? ix r> P la y ers , ma y be called G. 0, ■’ ■“> ' respectively, and the tournament will, of course, consist of 15 rounds, five on each link. Mr E. Craig sends this interesting problem, but his sugSd arrangement of pairs does not quite the conditions imposed. AN UNUSUAL BEQUEST. One frequently reads of curious condiuins,.and stipulations attached to chari-t----able bequests, and one which recently came und'er notice was of an unusual type. Besides endowments to the hospital and other similar institutions, one provision was for the payment on every Christmas fj oor families in the testator’s neighbourhood of a certain sum to each man and woman, with the singular condition that the number of men and women .should be dilferent at every distribution. Bu i the fact that bot h the total sum and the amount for each was specifically expressed in the will, a distribution could obviously be made ad infinitum provided the money held out, but as that condition limits the number of annual disbursements, let us make a little problem on the point. Supposing the total annual sum to be distributed was £55, each man to receive 50a, and each woman 30s, on how many Christmas days could the dole be issued under the conditions stated, if we stipulate also that the number of women must always be double that of the men? A TIME LIMIT. Here is a little problem which the reader will no doubt readily solve mentally and without leaving the fireside. A contractor had an urgent drainage contract with a 30-days’ time limit, ana put J ork on the job. But at the end of 24 days the work was oniy half completed, and to enable the contract to fulfilled he placed extra men on, and the full gang working at the same uniform rate as the first 15 men, completed the work in the specified time exactly. How many extra men were put on? LAST WEEK’S SOLUTIONS. "HAD, HAD,” ETC. The passage would be rendered inlelli--8} We by making two sentences of it. Tom although John had had "Had had,” had had Had. Had had” had had the approval of the inspector. Of course, alternately, Tom may have written Had had” and not John. The' passage evidently occurred in a review of two students’ examination papers. A GREENGROCER'S WEIGHTS. , 1 , 3 ® 2?lb weights would enable the dealer to carry on.” TWO FOR THE ARMCHAIR SOLVER Twice. (2) As February 10, 1960, will fall on Wednesday, the loan will become due on Saturday three days later. GOLD COINAGE. , .^i s n .25.7 dollars at 4s 2d are equal to f-x I xl x * . ounces is the smallest quan tity that could be converted into an oven number of sovereigns. GOLD AND SILVER COINS. Ten of each denomination mentioned. ANSWERS TO CORRESPONDENTS. "Dublin”—The “Irish Mile” is now obsolete. It contained as many yards are Pounds in a ton, viz.. 2240, e Compass " Boxing the compass " is naming the 32 points in their proper order, C. J. description will meet the case, though a diagram to scale would be better.