NUTS TO CRACK

Otago Witness, Issue 3996, 14 October 1930, Page 5

NUTS TO CRACK

By

T. L. Briton.

(For the Otago Witness.)

Readers with a little Ingenuity will find In this column an abundant store of entertainment and amusement, and the solving of the problems, should provide excellent mental exhilaration. While some of the " nuts ” may appear harder than others; It will be found that none will require a sledge-hammer to crack them.

Solutions will appear In our next Issue, together with some fresh “ nuts.*’ Readers are requested not to send In their solutions unless these are specially asked for, but to keep them for comparison with those published In the issue following the publication of the problems THREE SQUARE AREAS. Three blocks of land were each measured in the form of a square, though of different areas, the smallest being exactly 72 acres less than the next one in size, the difference between the latter and the largest of the three being 280 square chains less than 100 acres. Now if these three square paddocks had been so measured that each side of the largest had another chain added to it, and one chain taken off each side of the two smaller blocks, can the reader say what would be the area of each pcddock? Although this question is not one that the reader will perhaps elect to attempt without the aid of pen or pencil, the problem does not call for severe mental effort, especially when told that the combined areas of the “ new ” blocks are exactly 500 acres. AN USURIOUS STIPULATION. Sixty per cent, per annum was the somewhat exorbitant interest charged by a money idnder on a loan of £lBO for a period of four months. That was the contract agreed to between two parties, L and B, the former being the opulent one. A typically usurious stipulation, however, was afterwards made by the lender, and perforce, agreed to by the unfortunate-party B, namely, that .-art of the advance should be in the form of five dozen of wine at Is 9d per bottle, and an oil painting as an equivalent of £l9. Let us assume for the purpose of a little problem of utility that these goods cost L only one-quarter of the sum that he charged for them, and find what interest the borrower was actually obliged to pay for the advance, and how much cash he received from this modern Shylock, taking for granted that he followed the practice of usurers of taking the interest in advance.

RIDING IN TURNS. Two men travelling in a sulky drawn by a tired horse had an impossible proposition confronting them of reaching the railway station with their equipment by 4 p.m., it being then half-past 11 o’clock a.m. and the distance about 40 miles. A passing motor cyclist was hailed by the men, and after a parley an arrangement was made so that the men’s object would be achieved, the procedure being that the cyclist should give them alternate rides with him on his machine while one walked. It ro happened that in this way the men arrived at the railway station together at 3.45 p.m., and this fast invites a little problem. One of the men during his walking period travelled uniformly at five miles per hour, the other at four miles per hour, while the cyclist maintained an even rate of 20 miles per hour with one of the men aboard. Can the reader arrange a method of procedure which enabled the three men to arrive at their destination simultaneously at the time stated if they all left the 39-mile post at noon and made no perceptible stops en route? ENLARGING A PEN. Here is a little problem which may demand of the reader a moment or two of serious thinking, notwithstanding that the mathematical phase of it is quite elementary. A farmer had a sheep yard oblong in shape, constructed of 20 “ hurdles,” each five feet in length, the pen enclosing 135 hoggets, that number being the maximum that the yard would hold, on the basis of five square feet to every three animals. A draft of 240 additional sheep was expected that day, which were to be placed with the other hoggets (being of the same class), after the pen had been enlarged. But the farmer had no more “ hurdles ” ready, so he and his men set to work and made a number of extra ones. The question then for the reader to decide is, what is the smallest number of additional “ hurdles ” of the same size that are necessary to hold the two lots of sheep, assuming, of course, the new draft of hoggets is of similar size to the others, requiring five square feet to every three animals ? » HEFTY RAMS.

Whilst on the subject of these useful ruminants, let us have another “ hurdle ” problem. Six rams were placed in a pen made in oblong shape with eight “ hurdles ” five feet long and four feet high, three on each side and one at each end. As is necessary with this class of sheep, they had to be separated, so five extra hurdles of the same size were requisitioned, and the enclosure divided into six pens of the same size and shape, each of which was occupied by one animal. During the night one of the rams broke out, completely destroying

one of the hurdles. No extra hurdles being available, the farmer was able next morning, with only 12 of them, to make six new pens of equal size and of uniform shape, though of reduced area, and the problem for the reader is to discover how it was done, so that the six hefty rams each had the same amount of space allotted to him.

LAST WEEK’S SOLUTIONS.

OF SENSIBLE AGE. Prima 32 and secunda 23.

A REFRESHING PUZZLE. 1-1, 1-2, 2-0, 0-0, 0-3; 1-0, 0-0, 0-2, 2-1, 1-3; 4-0, 0-0, 0-2, 2-1, 1-0; 2-0, 0-0, 0-1, 1-3, 3-0. ; THERE AND BACK. One hundred and sixty-eight miles. r 'i WHO WON? . ; The distance was 50 yards, the three being “ dead heat.” MULTIPLIED AND ADDED. Three, and one and a-half is an ex.ample. The rule is that any given num? ber when multiplied by or added to 1 (one) and a fraction, of which the nume? rator is 1 (one) and the denominator one less than the given number, the re? suit will be the same. ANSWERS TO CORRESPONDENTS. “ Tides.”—Neap tides immediately fol.low first and third quarters of the moon, and their range is usually about one-third of spring tides. “L. E. W.”—Regret that the communis cation giving the name fully ha? been mislaid and not available a£ the time. Your favours appreciated. “Shares.”—Not intending to hold, but to sell at a premium.