INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20420, 23 November 1929, Page 6 (Supplement)

INTELLECT SHARPENERS.

BY li Tj. ÜB.ITDN.

WHAT WAS THE SCORE?

The whole eleven went, in to bat in the last innings of a cricket match, and all escaped the dreaded " duck egg." Though we have only the record of llic actual score of ono of these batsmen, details of the relative scores of five others aro available, and these the reader will find, no doubt, are quite sufficient to correctly answer the question, " What was the score 1 " Let us call the six batsmen A, 13, C, D, E, arid F, the la,tier's contribution of 21 being the only individual scoro knowq. A scored six-fifths as many runs as B made; 13, eleven-ninths as many as G scored; 0, five-fourths as many as D got; D, nine-sevenths as many as E scored; E, four-thirds as many as F, and F, three-fifths as ruany as the other five batsmen made. No details of sundries are given, but if there were five wider, six byes and three no-balls, can the reader say what was the scoro in the innings, and how many" runs did thc top scorer make 1 FIVE GOLF BALLS. In a box at the club-house there' were five golf balls, and as five players passed out, each took one after carefully examining it to see that it was his own. The incident, though trivial, prompted a question in " combinations " which involves an interesting calculation. Let us suppose that the five bulls were alike in every detail and not distinguishable by their respective owners without a careful examination of private marks. Assuming that the halls had been so marked, and that each player took one at random, what are the chances that every one would take the wrong ball, that is" to say that each golfer took a ball that belonged to one of the other four players ? MILKMAN'S "EASY MONEY." A milk vendor bought pure milk at Is lOd per gallon, and after adding water to it sold the mixture for 7d, a quart. The evidenco showed that he had put five parts of water to every 23 parts of milk. If a week's supply of pure milk costing £25 13s 4d were adulterated. in this way and sold at 7d a quart—the price at which the pure article should have been retailed, what were his profits over and, above the profits ho was entitled to ? INVESTMENTS IN COCO-NUTS. Three capitalists invested in an island coco-nut property, and after planting the area the total monev laid out, including buildings and copra-drying machines, wa3 £15,000, X investing £2500, Y £SOOO, and Z, £7500. The partnership agreement contained the condition that the whole of the net profits should be divided in such a way that the rates of interest that each received would be in the proportion of the amount invested. As these palms do not come into bearing for seven years after planting, each investor received five per cent, per anriflm on his capital for those years, but if the net profits after this deduction were £2450 in the first year of production, how should the money have been allocated between the three in terms of the partnership agreement. SIMPLE QUESTIONS. It is not always the case because i question is a simple one, particularly where figures are involved, that everyone concerned is agreed as to the correct answer. Speed problems and those concerning averages are cases in point. For example ; A motor-car travels around a circular track at two different speeds, viz., the first half at a uniform rate of 50 miles an hour, the other half at an even rate of travelling at 20 miles an hour. It is a very simple calculation to. .find the full distance travelled, when told that the time occupied in the round was exactly three minutes, but how many readers can give the answer right of! ? Of course, the distance could be in a straight line " there and back," so flie mystery of circles and diameters may be ignored.

LAST WEEK'S SOLUTIONS

Thriity Clerks

The respective earnings in five years of A and B were £350 and £362 10s, so, if the former saved £37 10s, . representing one-quarter of his earnings, B (to sava twice as great a proportion as A, namely one-half), must have been thrifty to the extent of £lßl ss, the combined savings being £268 15s, as stated in the problem. Concerning Ages. (1). 2.1 and 12. (2). In four and a-half years, making their respective ages 13£ and 40j. a— Two Cyclists. The distance travelled by the other cyclist from the house to tho roadman's tent and back was 15 miles, 704 yards. 4n Interesting Sprint. The boy's strides were uniformly Ift. ii% length. Three Investments. Five " Forests " at £lO each, 95 "Breweries " at £SO each, and 400 " Coals " afj 10s each.