Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21473, 22 April 1933, Page 5 (Supplement)

Intellect Sharpeners

TWO FOR THE ARMCHAIR

By T. -X- BRITON

Ono of the batsmen in one of thek recent test cricket matches made a scoro of exactlv a century in his two innings, one of which was " not out." This number of runs was made in the batsman's 19th innings of the season, though he had been to the crease on 20 occasions, the " not out " in this match indicating, for the information of the non-cricketing reader, that 100 runs were made in technically one completed innings, the 19th for the season* The average of the bastman was thereby increased by three runs, and tho question is what was his average after making the score referred to? One of tho first-grade soccer teams, before tho last game of the season, had a record of 3.4 in favour and 3.6 against. They won the final game by five goals to two, and this achievement made their goal averages equal, for and against. Can the reader say how many matches this team had played altogether during the season? These two questions may be readily answered without the aid of either pen or pencil. MIXING THE WINES A merchant grocer has 15 gallons o'f two grades of " Chablis," one keg of four gallons and another of 11 gallons, the latter being the inferior grade of the two. Ho mixes the wines in order to make a liquor of an intermediate grade to sell at tho rate of 28s a gallon. The better of the two grades was priced afc £1 15s 4d a gallon. If the merchant disposed of the 15 gallons after mixing, and received for it (at 28s a gallon), the same money as he would have received by selling the wine at the fixed prices for the two grades, can the reader say what was the selling-price of the inferior grade per gallon ? TRADING TRANSACTION A grocer professes to retail certain goods sold by weight at a margin of only 10 per c-pnt above cost. He, however, adulterates them with one-fourth of their weight of an inferior grade of article which cost him ' exactly twothirds of the price per pound that tho better grade of commodity cost him.. There are two questions that may be answered, probably from the armchair, if the reader so elects, from the few details related, first how much per cent profit would the man actually make in such circumstances, ignoring fractions if any, and in what proportions must he adulterate the goods which cost him the relative prices mentioned, in order that a profit of 50 per cent be made ? The reader will, of course, keep in mind that " profit " is based upon cost and not selling-price.. P COUNTING THE NUTS A greengrocer purchases two bushels of hazel-nuts, which his little boy, at his own request, was allowed to count. The result of the boy's counting was that the greengrocer found that the nuts' had cost him at the rate of 49 for twopence, so he then set the lad to divide the nuts into equal parts, which he shortly afterward 6old in two lots, one at the rate of 24 for a penny, and the other at a cheaper price, the rate being that the second buyer received an extra nut for every penny the half-lot realised. The total number in the two bushels was the least number possible for ther - greengrocer to purchase with the stipulation that he spent an integral, that is to say an even number of pence in the purchase, and this feature applied also to the number of pence he received from each of his two customers. The boy was rewarded to the extent of one penny from the profits made by the greengrocer. The three questions arising from the statement are: First, how many nuts were in the two bushels?, Second, what did they cost? Third,; how much did the man make in th/ whole transaction?

DIGITS AND LETTERS Of all the methods of writing messages in code, the plan of using a combination of digits and letters is probably the least favoured in important communications, notwithstanding that this method of sending messages has the advantage of being able to be quickly composed and of being as rapidly read by the person for whom the communication is intended and who is possessed of the key. Here is a passage in this form which may provide the reader with quite half-an-liour of mental exercise in converting it into intelligible English, the obscurity of the key to the puzzle being ample, probably, to test his ingenuity. The whole of the nine digits as well as 17 letters of the alphabet are used in the code, and when. each has been given its correct equivalent a. sentence of 30 words in good English, will be revealed. DQCN 7TTNG 87G83N Cl 5 4T3H CI3S QDCN K7IBjSTDNG 4SQ DCQN 4£CM> JTQR DCJJGS4GN CI3S £CNQ 87G89BSNONT8N DC492C QT6 DQNC S4GBNG GIT 134T2 NQCD 37TN Q?D 6493R CIPN DG4 GNP439D74T5 1354. The letter " I " does not appear iut the code, so the digit " 1 " cannot be> confused with it. LAST WEEK'S SOLUTIONS Age ol a Family.—4B, 36, 12 and 4,, Tho " average " paradox arose on account of there being only three in thepicture 10 years ago. , , Poultry and Grocery.—The price of the gooso was 10s, and for a duck, Bs«j (2) The two instalments were £22 10s., nnd £67 10s, the difference being halir tho sum Stepping the Distance. —As the man. ! who travelled north, covered, & dist&nco i of 400 yards, just double tho length, stepped by the other, the latter musl* have arrived two minutes before hia. colleague. Two Money Questions. —(1) Tho two men must have commenced with £•> each one having and tho other sit the finish. (2) The amount of tho guarantee was £l2O, so that the fn ° had to pay £24 each, instead of £2O an arranged.

answers to correspondents

A.D.l).—Thanks. Arrived while on furlough. " Mark." —A skeleton of the L.D, sum has been forwarded. " Colenso —Much obliged and it will be looked into at first chance. " West Coast."—Thanks, but it La:i been well threshed out in this column. 15 (<—y oSi 1 quite agree, but hope duties not so strenuous that they will prevent despatching an occasional communication. " X.Y.Z.''—-It is precisely the samu thing reversed, with the first figure moved three places forward, the last digit moving back similarly. "Bessie". —The puzzle referred to is not soluble mathematically, but ills can be done by using a little artifice which has confused others also. X.Y.Z. —The question did not involve an algebraical calculation, bub merelv one of finding by logical deduction, the respective equivalents or the letters used. " Polar." —Latitude 77deg. 235. south, and longitude 166deg. h3m< 245. east, tho position being many de r frees west of New Zealand. IUII. (3) Scott. fl| 1