Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21278, 3 September 1932, Page 5 (Supplement)

Intellect Sharpeners

ALPHABETICAL ARITHftETtCP _ . . i. : ■ a&i; BY T. L. BRITON Although the letters XYZ and their?* companions in the following problem, are quantities, the reader ' who is. not partial to the section of mathematics which treats of these mysteries, may safely proceed to solve "the problem, which ra« quires merely the exercise of his Each of the nine letters used represents 4 digit which, added together, total 45, and the puzzle is to find the numerical equivalent of each letter from a perusal of tha alphabetical expressions given. " the sender of the puzzle, states that it was suggested by another which appeared in this column some timo ago, and as in. that case it should be noted that letters when placed together must be arithmetic cally translated at their individual values., VW does not. mean as in algebra that Vj is multiplied fey W and mean 35, if the equivalent of V is seven and W is five, but the two letters so written would ba| translated as 75, and so on. XR, multiplied by S, makes a product VZTJ. TW minus Z makes XY, and if XRS and W beseparately added together the total is tha samo as when T is multiplied by Z. What arc the respective equivalents of the nins» letters ? . <

FOR THE ARMCHAIR Mrs. Jone3 has a small boarding the normal number of guests being only five, eight constituting a " full honse " ofboarders. Sho is a very careful managerand keeps a correct record of every item' of receipts and expenditure, knowing: exactly how both sides of her ledger varyas the number of guests change above and below the normal strength. For example, she knows that an addition of three> boarders above the normal number increases her annual expenditure by £96, but at the same time it diminishes tha' actual annual cost per head by £3, that is for the eight, not the extra three only, as compared with the cost per head when five only are in residence. Can the reader:.' say what is the annual cost when the normal number only is on the books ? CURIOUS PUZZLE Problems like the following are always useful, and many of them, though apparently simple, are not a little perplexing,, giving the would-be solver Bome moments, of hard thinking before the puzzle is unravelled. A man has a two-gallon jar full of pure spirit, from which he drawß off a jugful and places it in another empty, vessel. He then fills up the original jar of spirit with pure water, and after thoroughly mixing it he draws off another jugful of the mixture, filling up the jar again with pure water. The question is if the contents of the jar are then in equal parts, of spirits and water, what is the size of! the jug that the man used? As its: capacity must be greater than one quart,, the answer to the nearest gill (quarter* pint) will be sufficient. FROM WOOL TO BUTTER A sheepfarmer, owing to the low prica\ of wool, decided to sell his stock and purchase a herd of dairy cows, and instructedl his agent to attend to the matter for him,,the former thereupon - giving the job of: getting a herd together to a cattle dealer... It was agreed between the agent and the. dealer that the former supply the money/ necessary and receive ten per cent on thai total cost of the cpws as paid by thd> dealer, the agent charging the sheepfarmepa price for them slightly higher than what, was paid for them. The dealer paid tha--ten per cent, all expenses of travelling to> the various localities, also the cost of drov--ing and other incidental expenses, re* ceiving in return for his work the difference between the actual price paid for the cattle and that which the agent charged the farmer for them. Forty-eight head were bought altogether at an average price, of £ls 12s 6d each, and tha farmer paid for this number as follows: —Fourteen at £l2 10s each; ten at £l4 Is 3d each; nine, at £2O each; and fifteen "studs" at. £2B 2s 6d each. If the dealer's expenses amounted to £2 10s more than his net. profit, how much did the dealer make* out of the transaction? ,

EQUIDISTANT COUNTERS Here is an interesting problem which\ the reader may .p.f-sibly find new, particularly when the solution is limited to one. by the addition of a condition that, is; absent from the orthodox puzzle of tha kind. Take ten counters or coins, and place them in a row. It is required to> move the pieces according to the following; conditions so that the ten shall be arranged in five equidistant conples, the top ones adding up to the smallest possible total. Make a diagram of ten equal spaces in a row and number them from the left,, one to ten, placing a correspondingly, numbered counter in each of the ten, places. Any counter may be moved in either direction over not more than two others adjacent to it, anß placed upon tlia counter next beyond the counters thus jumped over. Thus, nnmber seven may be moved over number six and placed upon number five, or may be moved, over numbers six and five and placed on the top of number four. And th®> same on the other side of the countermoved. At the finish the five pairs musti, not only be equidistant, but the five top' counters must add up the lowest possiblei total under these conditions. Can th»> reader do this in less than five moves? t ~v LAST WEEK'S SOLUTIONS Age of a Fair Maid. —Bom in 1918. Exchanging Scrip.—Smith COO, Jonew. 900, and Brown 1300. Two More Partners.—" A " £l<ls'6* " B " £440, and " O " £64. Total, £1960* Good Price For Wool.—The digits, 1, 2, 3, 4. 5, 6, 7, 8, 9, being the re«spective equivalents of Z, X, S, V, R, W,, Y, U, T, the price per pound for wooJi. h 25d. Hunter and Hare.—Five seconds elapsed, before the first shot was fired. If tha reader found that the man fired a second time it would be correct if the time deter*, mined is eleven seconds. But the question stated " the first shot." ANSWERS TO CORRESPONDENTS " Curious ".—Quite suitable, thanks. F.J.W. —Thanks, but has already appeared. " Bittern —Letter went astray* Thanks for interest. " R.M."—Extra conditions introduced, designedly, and not essential to solutions. (2) Intended in the main nontechnical reader. - ' A.B.C. —Your methods are quite correct but you went slightly astray in the calculation which you will no doubt note if looked through again. ( "Legal" The only results known to. be authentic are with eight sets, which will permit of any integral number up. to 40 being so weighed. > . erratum In the alphabetical sum, August 27, Ui* words namely twenty-five advertently omitted follow ng P