NUTS TO CRACK.

Otago Witness, Issue 3831, 16 August 1927, Page 23

NUTS TO CRACK.

By

T. L. Briton.

(For the Otago Witness.) Headen with a little ingenuity will find in iis column an abundant store of entertalnmerf and amusement, and the solving of the problems should provide excellent mental 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 1n our next issue together with soma fresh "auts.” Readers • re 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. ON THE HIGHWAY. Although the incident occurred in the old days, when the main roads of the Dominion served also as travelling stock routes, the facts are none the less interesting for problem purposes. Two men, A and B. were long-distance cyclists, and were riding along the main road to the city, A being a considerable distance ahead of the other. They both rode at exactly the same rate. At the fiftieth mile post from the city A overtook a flock of sheep which travelled at the rate of three miles in two hours. Two hours afterwards he met a mob of cattle travelling at the rate of nine miles in four hours. B overtook the sheep at the forty-fifth mile post from the city, and met the mob of cattle exactly 40 minutes before he came to the thirty-first mile post. Can the reader deduce from these facts the actual distance from the city B was at the moment at which A arrived there ?

A SCHOOL’S ENROLMENT. In a certain country school the total enrolment was less than 100, excluding the infants, and there were no pupils in Standard I. The number in Standard II was one less than a third of the number enrolled in Standard V, and three less than half the number in the senior Standard VI. Those in Standard HI, together with those in V, outnumbered the total pupils in both Standard IV and Standard VI by three, and those in Standards IV and V combined numbered exactly one less than half the whole enrolment. As the total in Standard VI, added to those in Standard IV, represented seven-sixteenths of the enrolment of the five standards mentioned, one of which contained one-quarter of thq total, how many pupils were enrolled in each of the standards respectively?

DISCS AND SOLID SPHERES.

As the reader is aware, the largest number of discs laid fiat that can be placed around one of similar size, so that each of them touches it, is six. Is there any difference, if the dises were perfect spheres of the same diameter? And, assuming that those were solid spheres, and that the area of the surface of any of them contained exactly as many square inches as there were cubic’ inches in its volume, what would be the length of its diameter? (By the way, it must have been a cannon ball, for it weighed 14 pounds) ? -A knowledge of ratios of diameter to circumference, area or volume is not required to enable this problem to be solved, but just elementary mensuration. Still it will require a little thought to discover how to proceed via this simple wav.

COUNTING SOVEREIGNS.

Readers are aware that weighing instead of counting is the usual method in mints and large banking institutions for determining the number of sovereigns in large quantities, though it is not practicable, nor expedient, perhaps, in the ordinary way oi banking business over the counter. In some countries the custom in banks is for tellers to have at hand gold coins in sealed bags marked with the exact amount of contents ready for paying out without the trouble of counting c” weighing. The bags are made up in sums that will enable any amount in gold to be paid by handing out one or more bags. Sunposing these coins were sovereigns, what sum should each of eight bags contain so that the exact amount called for from one pound to two hundred could be paid in this way, without giving more than one bag containing the same sum? SCOTLAND YARD. Scotland Yard was able to sheet home a charge of niurder (afterwards confessed) by a very simple A roblein in mathematics. It was in the ease of a murdered steward whose body was found in the Thames some months ago. It appears that everything depended upon proof of the exact time the niurder took place, but before the police reached the scene one of the watermen who e ound the oody took the murdered man’s watch (broken by the blow) from his pocket and turned the hands around to try if it would go. When the detectives heard this they were not baffled, for though the waterman could not remember what time the hands showed he knew they >.«-re both together, appearing as if there was only one hand, zis the evidence had narrowed the time of the murder to the hours between quarter after midnight and 2 a.m. the detectives were thus able to determine tl.e exact time the blow was struck. What time was it when the watch stopped? LAST WEEK’S SOLUTIONS. THE FARMER’S WALK. The mailman was correct, for by leaving the mail at the gate instead of in the box the farmer was saved nearly five chains walking. A GRAZING PROBLEM. The more practical method of tethering the goat on the circumference so that it could graze on exactly one-half the area only of p..ddock would be to make the tether the exact length of the radius and fix it at any point on the circumference. When that area is eaten off

move the peg to a point one eighth of the length of the circumference further away, and the goat will have access to exactly one-half of the area, part of the latter tether giving it access to a part previously grazed. TWO HOOPS. The circumference of the hoop being 13.69 feet, it would travel 1309 feet in 109 revolutions, based on the differences stated—viz., 9 inches and 5 inches. THE HERVE SQUARE. 41 8 213 5 7’ 7£ 2 51This square conforms to the conditions ana adds up 15, horizontally, perpendicularly, and diagonally. TWO POLES. The crossing point of the two lines must have been 12 feet from the ground. The distance between the poles does not make any difterenee. ANSWERS ‘TO CORRESPONDENTS. 1 J -M.—Quito corrcct - With 100, it would be 19, 1 80 only. See Otago Witness of August 2. C. E. C.—A die according to Hoyle should be numbered in that way only, N. C. It is a novel way certainly and quite interesting, but somewhat lonely. r C. B.—No doubt there are tea-tasters employed professionally in New Zealand as in other countries, but it may be questioned whether there arc- apprentices in the business.