NUTS TO CRACK.

Otago Witness, Issue 3832, 23 August 1927, Page 51

NUTS TO CRACK.

By

T. L. Briton.

(For the Otago Witness.) Reader* with a little ingenuity will find in ils column an abundant store of entertainment and amusement, and the solving of the problem* should provide excellent mental exhilaration. While some of th* “nuts” may appear harder than others, it will be found that none will require a sledge-hammer to erack them. Solutions will appear in our next issue together with some fresh "aut»." Reader* - re requested not to send in their solutions, unless these ar* ipecially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. A FLOOD RESULT. The heavy winter rains in the country caused a number of quarries and other excavations to be floooded, and the work of baling out was necessarily slow, being mostly done by man-power. One large cheese factory cellar, of exactly 500 cubic feet capacity, was not quite full of water, but less than another 50 gallons would have made it overflow. More than half the quantity of water was emptied the first day, but in the morning there was exlictly double what had been left by the men, owing to the percolating nature of the soil. On the second day the same quantity was pumped out as on the first, but next morning there was three times as much water as the men left the evening previous. On the third day T he same quantity was baled out as on the first and second days, but on the next morning there was four times the quantity that had been left. The fourth day found tho same volume pumped out as daily before, but next morning there was five times as much in the cellar as the. men left the evening before. On the fifth day the men pumped out exactly the same quantity as on each of the other days, and thus emptied the cellar. How much water was in the cellar when pumping was commenced ? A BEQUEST. A bequest of £4OOO was to be divided between two charitable institutions —one, the hospital, receiving the larger share. In a year the hospital gained a certain rate per cent, on its portion, while the smaller share, by more fortunate investment, gained two per cent, per annum more than the other. The joint gains in this way were £268 In the year. If, however, the hospital had secured the percentage that the smaller portion obtained, and the latter had obtained the lower late, the total amount of interest for the full year by the two investments would have been £292. How was the bequest divided between the two institutions?

BROKEN TIME. A skilled mechanic in a foundry receiving four shillings an hour was frequently called away on business that concerned only himself. This irregular practice was tolerated by the manager, until it was found that the mechanic spent most of his time away from the.foundry. His employment was therefore terminated. As his outside private work was not sufficient to keep him, the mechanic offered to work at the foundry for more than half the regular hours, which were forty-eight per week, and to receive the usual four shillings per hour for all time worked, agreeing to forfeit five shillings per hour for the time away from the foundry during working hours. This was agreed to, but at the eml of the first, week he had only seven ami sixpence’ to draw. How many hours 'lid he put in at the bench during the week? UNORTHODOX. Although, not. infrequently, readers have written to say how much more they enjoy this column than crossword puzzles, one of these latter problems is being included this week, because it is not. of the orthodox variety Each space is to be occupied by a letter of the required words, and as there are consequently no 'blocks,” a diagram is not necessary. Down. Across. 1. Grocers stock them 1. To tall into a 2. Parts of the sloping posture human body. 5. To raise one end 3. Contained in a of furlong. 9. A thrust 4. To vex, to annoy. 13. An awning in a boat. AVERAGES. The calculation of averages and percentages is a part of elementary mathematics always liable to provide pitfalls for young students, simple as the solutions are. A little problem, published some time ago, concerning the average rate of speed that a motor car makes if it runs at a uniform rate of 20 miles an hour on the outward journey, and 30 miles an hour returning over the same road, gave rise to much controversy, and still some people declare the average to be miles I per hour. But then we all know of the existence of people, societies, etc., which still contend that the earth is flat. A more puzzling curiosity concerning averages than the motor ear speed is that concerning bowlers’ cricket averages. Can tlie reader discover an example (and there are many) where A, a bowler, gets a ! better average than B in each of the two [ innings, yet the latter secures the bowling trophy for the match by obtaining the ■ better average? It is worth pondering ; over.

SOLUTIONS OF LAST M EEK'S PROBLEMS'. ON THE HIGHWAY. B must have been 25 miles from the city when A arrived there. A-SCHOOL’S ENROLMENT. In the five Standards 11, ITT, IV. V, and VI there must have been 7, 14. 15. 24, and 20 pupils respectively. DISCS AND SPHERES. (1) There is no difference between the number of discs and spheres under the conditions stated. (2) The diameter must have been six inches, because the square of the diameter of any square 1 multiplied by a certa’in factor

area of its surface, and the, cube of the diameter multiplied by one-sixth of the same factor gives its volume. The value of the factor is immaterial. COUNTING SOVEREIGNS. If the eight bags contained respectively 1,2, 4,8, 16, 32, 64, and 73 sovereigns, any sum required, up to the maximum of what they all contained, could be paid out by giving one or more bags of different sums. SCOTLAND YARD: WHAT TIME WAS IT. There are several times in twelve hours when the hands of a clock are together. The one coming within the period stated is smin 27 3-llsec past 1 a.m., which is, therefore, the time the watch stopped. ANSWERS TO CORRESPONDENTS. T.P. — ‘‘The farmer’s walk.” The alternate routes were (1) from where ho was working, W, to the gale, and thence to the house; and (2) from F to the house via the mailbox. C.D.—The method was fully explained by postcard. Your viewpoint inferred that actual lengths were at issue, but that was not so as you have now seen. W.C.S.G. —Your continued interest is much appreciated.