INTELLECT SHARPENERS.

New Zealand Herald, Volume LXV, Issue 20112, 24 November 1928, Page 5 (Supplement)

INTELLECT SHARPENERS.

TWO MINING PROSPECTORS.

BT T. I* BRITON.

Ben and Jim, two mining prospecto; s, were camped at a creek about 100 miles south-east from tbo mining warden's office, which they were obliged to ctterid recently, and together they .walked there, in two and a-half days. Let us make a little problem on their journey back to camp. Ben left the warden's officewhich was situated in tho exact centre of tlio 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, and duo east from the mining office, hence 80 miles direct south to the camp from which they both set out week before. Jim, having other busii f to transact, started from tho warden k office exactly llh. 6m. 40s. after Ben's departure, and travelled direct to the camp by tho same route as they came, both men arriving there at the same time. Assuming that eiich maintained his own speed uniformly throughout, at what rates did they walk respectively ? DEPTH OF A WELL. Some weeks ago a probley appeared in this column entitled " A Holo and a Pole," the solution of which was published a week later. A correspondent signing himself " Digger " now states that lie has calculated tho depth of tho unfinished well and found it to be 36ft., and not 27ft. It is not surprising that soma difficulty would bo experienced in arriving at the correct solution, for the statement of tho question was liable to be misread, so hero is the explanation of the calculation to enable " Digger " to see his error. At the first measurement the 15-foot pole when placed upright in tho unfinished well showed 6ft. above the ground. The problem stated that the hole then had to bo yet dug " twice as far," which meant, of course, 18ft. more, which added to the 9ft. makes 27ft., the full depth wher completed. Tho proot of this is that the top of the pole would bo 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 appreciate!. ALL ABOUT ADA. A novel little puzzle as distinct from problems has been received from " Waihi." He asks in how many different ways can the word ' Ada '' 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 uot be used twice in the one word; and second, that the word should be snelt 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 quito possible _ for the reader to considerably underestimate the number of different ways the word can be spelt under tho stated conditions. There is, however, a very simple arithmetical formula for it, 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 ?

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. After 30 minutes three discharge pipes are then opened together and exactly three hours and 50 minutes after the supply pipe was opened the four pipes are closed simultaneously. If, upon measuring the quantity of water then in the tank, 't is found that exactly 75 more gallons will completely fill' it, can the reader say how many gallons thn tank will hold when full ?

A GAME OF DOMINOES. Three persons, A, B and C, were engaged in a gamo of dominoes for small lfivel 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" iti his tuni 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 "C" had won fourpence, and that*each of tliem had exactly the same sum though they started with different amounts. The question is what did uacli player start with ? LAST WEEK'S SOLUTIONS. A Deal in Eggs. Tho poultry-farmers must havo had five and a-quartcr dozen eggs to sell to tho six women, who bought respectively 32, 16, 8, 4, 2 and J. Filling a Cistern. Under the conditions stated the timo occupied in filling tho 53-gallon cistern was threo hours 50 minutes. Ages of Jack and Jill. Jack and Jill wore twins, born in 1822, and thus were 16 years of age in 1838 Spent One-half. „ The gentleman started out with 12 one pound notos and 16 shillings ant l tool* homo 12 half notos and foui florin- (' one-half tho amount he had with Inn Sports Prizes. Group A won prizef to'the vniii' £lO, B £ls, and C £5. ANSWERS TO CORRESPONDENTS W.S.C.G.—Many thanks. T.D.—The chances °* Ambers in six, not four, and even if U had been eight fourteen tho would bo precisely tho same. •' Paradox."— It «s undoubtedly where it i> Mir . .. "Money Order."-The annuity- table rcpZWmoW 't ll.re. per «. _ S.P.-AO WW palpably .by »abstltutto* five for