NUTS TO CRACK

Otago Witness, Issue 3898, 27 November 1928, Page 69

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. TWO MINING PROSPECTORS. Ben and Jim were mining prospectors who had worked together for many years. The distances they had tramped in quest of the precious yellow metal lok on paper more like the records of a motorist. They were camped at a creek about 100 mile's south-easCMrom the mining warden’s office, which they were obliged to attend recently. Together they walked there in two days and a-half. Let us make a little problem on their journey bac.. to camp. Ben left the warden's office (which was situated in the exact centre of the circular-shaped district) on a prospecting expedition, travelling due north to an old mine five miles outside the circumference of that zone. From here he walked south-east to an abandoned shaft situated 20 miles outside the circumference, due east from the mining office, hence 80 miles direct south to the camp from which they both set out a week before. Jim, having other business to transact, started from the warden’s office exactly 11 hours 6 minutes and 40 seconds after Ben’s departure, and travelled direct to the camp by the same route as they came. Both men arrived there at the same time. On the assumption that each maintained his own speed uniformly throughout, at what rates did they walk respectively ? THAT WELL. Some weeks ago a problem appeared in this column entitled “A Hole and a Pole,” the solution of which was published a week later. A correspondent, signing himself “ Digger,” now states that he has calculated the depth of the finished well and found it to be 36ft, not 27ft. It is not surprising tha*- some difficulty would be experienced in arriving at the correct solution, for the statement of the question was liable to be misread. Here is the explanation of the calculation to enable “Digger” to see his error. At the first measurement the 15ft pole when placed, upright in the unfinished well showed 6ft above the ground. The problem stated that the hole then had to be yet dug “ twice as far,” which meant, of course, 18ft more, which added to the 9ft, makes 27ft, the full depth when completed. The proof of this is that the top of the pole would be then 12ft below the surface of the ground, or twice as far as it was above when first measured. Digger s keenness in raising the question is appreciated. ADA. A novel little puzzle as distinct from problems has bgen received from “Waihi.”' He asks in'how many different ways the word “ Ada “ can be read from the letters arranged as shown in the diagram below. The conditions attached to the query are, first, that the same “A” must not be used twice in one word; and, second, that the word should be spelt from any of the eight “ A’s ” to the D; and thence to any other “A,” whether it be diagonal, horizontal, or perpendicular. Though the puzzle is not a difficult one, it is quite possible for the reader to under-estimate considerably the number of different ways the word can be spelt under the stated conditions, there is a very simple arithmetical method of finding this, which will obviate the necessity of solving the puzzle by trial.” “ Waihi ” calculates that the number of different ways the word can be thus spelt is 56. Can the reader improve on this?

THE CAPACITY OF A TANK. Here is a simple and useful problem requiring ’no knowledge of mathematics beyond that taught in the Sixth Standard:—An empty tank has a supply pipe which can exactly fill it in two hours, and also three discharge pipes which, separately, can empty the full tank in 12 hours, 10 hours, and six hours respectively. Let it be assumed that there are exactly 75 gallons of water in the tank when the supply pipe is fully opened. 4fter 30 minutes the Yhree discharge pipes are opened together, and exactly three hours and fifty minutes after the supply pipe wqs opened the four pipes are closed simultaneously. If, upon measuring the quantity of water then in the tank, it is found that exactly 75 more gallons will completely fill it, can the reader say how many gallons the tank will hold when full? A GAME OF DOMINOES. Three persons A B and C were engaged in a game of dominoes for small level stakes, all the coins being placed upon the table. A lost the first game which resulted in doubling the sum that the other two had in front of them. B lost the second game, and this also resulted in the money held by the other two being doubled. C, in his turn, lost the third and last game of the series, and curiously it resulted in the doubling of the

sums held by A and B. Upon counting up their money it was found that U had won fourpence, and that each of them had exactly the same sum though they started with different amounts. The question is: What did each player start with ? LAST WEEK'S SOLUTIONS. SOLD OUT. The poultry farmer must have had five and a quarter dozen eggs to sell to the six women, who bought respectively 32, 16, 8,4, 2 and 1. FILLING A CISTERN. Under the conditions stated the time occupied in filling the 53-gallon cistern was 3hr 50min. THE AGES OF JACK AND JILL. Jack and Jill were twins born in 1822, and thus were 16 years of age in 1838 SPENT ONE-HALF. The. gentleman started out with 12 one pound notes and 16 shillings and took

home 12 half notes and four florins, thus spending exactly one-half of the amount he had with him. SPORTS PRIZES. Group A won prizes to value of £lO, B £l5, and C £5. ANSWERS TO CORRESPONDENTS. W. S. C. G.—Many thanks. T. D.—The chances of winning were one in six, not four, and even if the numbers had been eight and 14, tlii « e ‘ la . nce ,® "'oiild be precisely the same. laradox.'—lt is undoubtedly the correct solution.^ —Refer to issue of July ( 31, where it is full}’ explained. “Money Order.”—The annuity table represents money at 3 per cent. S P.—-Palpably an error, substituting five for six.