"NUTS!" INTELLECT SHARPENERS All rights reserved.

Evening Post, Volume CXV, Issue 94, 22 April 1933, Page 7

"NUTS!" INTELLECT SHARPENERS All rights reserved.

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Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of th» problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, it will bo found that none will require a sledge-hammtg to crack them. TWO FOR THE ARMCHAIR.

One of the representative batsmen in the recent Test match made a score of exactly a century in his two innings, one of which was "not out." This number of runs was made in the batsman's nineteenth innings of the season, though he had been to' the creases on twenty occasions, the "not out" in this match indicating, for the information of the non-cricketing reader, that the 100 runs were made in technically one completed innings, the nineteenth for the season. The average of the batsman was thereby increased by three runs, and the question is what was his average after making the score referred to? Here is a little football poser, taking the Soccer game instead of Eugby for a change. One of the first grade teams before the last game of the season' had a record of three decimal four in favour and three decimal six 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? ,As dndicajted in the title of these, two questions,, both are simple enough to be readily answered without the aid of either pen or pencil. . MIXING WINES. Here is a question of a kind met frequently in every-day business, even though the commodity concerned may not be in general use. A merchant grocer has fifteen gallons of two grades of "Chablis," one keg of four gallons and another of eleven gallons, the latter being the inferior grade of. the two. He mixes the wines in order to make a liquor of an intermediate grade to sell at the rate of ' twenty-eight shillings per gallon. The better of the two grades was priced at one pound fifteen, shillings and fourpence per 'gallon (£1 los 4d), and the question is if the merchant disposed of the fifteen gallons after mixing, and received for it (at twenty-eight shillings per gallon), the same money as he would have received by Belling 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? This is a very simple question which quite possibly the reader will elect ta answer while sitting in his armchair, A TRADING TEANSACTION. In the reported case of a tradesman who had been adjudged guilty! of dishonest practices in. connection with his business, with a consequent loss to his customers, details of the large and unfair .gains made in this way were revealed. Let us assume such a case in, which a grocer by advertisement and otherwise, professes to retail certain goods sold by weight at a margin of only 10 per cent, above the price the goods cost him. He/however, adulterates them with one-fourth of their weight of an inferior grade |of article, which cost the, tradesman exactly 2-3rds (two-thirds) of the price per .pound -that; the better grade of commodity-costs him. There are two questions that may be answered, probably from the armchair, if the reader so elects, from the few details1 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, may be made? The reader will, of course, keep -iir mind that "profit" is based upon cost and is not calculated in the perhaps more expedient way upon selling price. COUNTING THE NUTS. Here is an incident of a greengrocer purchasing a couple of bushels of hazel nuts, which his little boy at his own request was 'allowed to count, and simple as the questioft. concerning this matter is, the trader may find that before he has correctly answered it, quite a lot of hard-thinking has been found necessary. The result of- the boy's counting .was that the greengrocer found that the nuts had cost him at the, rate of- forty-nine for twopence, so he'then set the lad to divide the nuts into two equal parts, which he shortly afterwards sold in two lots, one at the rate of twenty-four 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 halflot realised. It so happened, that the total number in the two bushels was the least number possible for the greengrocer to purchase with the stipulation that he sp^nt .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 the two customers who bought from him. The boy was rewarded for his work of counting the "nuts to the extent of one penny from the profits made by the greengrocer, and the threq interesting questions arising from the, statement are, first, how many nuts were in the two bushels; -second, what did they cost; and, third, how much did the man make in the whole transaction? WITH 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 possessed of the! key. Here is a passage in this form frhich may provide the reader with quite half an hour _of mental exercise in converting it into intelligible English, the obscurity of the key to the puzzle being ample, probabiy, to test his ingenuity. The whole of the nine digits as well' as seventeen letters of the alphabet are used in the code, and when each has been given its correct equivalent, a sentence of thirty.words in good English will be revealed. ' DQCN 7TTFG S7GB3N Cl 5 4T3H CI3S QDCN B7IBIONG 4SQ DCQN 4DCNG' ITdR DCNGS4GN CI3S DCNQ' 87G8f)BSNGNT8N, DC4<I2C Q7S DQKC S4GBSG GIT 134T2 NQCD 37TN Q7O 649JE CIPN D 64 GNP439D--74T5 1354. i The letter ",I" docs not appear in the code, so tile digit "1" cannot be confused with it. LAST WEEK'S SOLUTIONS. An Armchair Poser.—4B, 36, 12, and 4. The "average" paradox arose on account of there being' only three in the picture ten years ago. Two Simple Questions.—The price of the goose was 10s and for a duck 3s. (2) The two instalments wero £22 10s and £67 10s, "tie difference being half the sum. ■ Stepping the Distance.—As the man jrho trayeUecl fibrth covered a distance

of four hundred yards, just double the length stepped by the'other, the latter must- have arrived two minutes before his colleague. Two Money Questions. —(1) The two men must have commenced with £5 each, one having £ 8 and the other £2' at the finish. (2) The amount of the guarantee was £120, so that-the five had to pay £24 each ihstead of £20 as arranged.* A "Restoration" Puzzle. —Omitting the "four" in each of the first two lines of multiplication, this problem would have four ' solutions, namely, divisors 846, 848, 943, and* 949, with respective quotients 1419, 1418, 1418, and 1416, but with the stipulation of two more "fours" in certain places the first quoted example is the only one.

ANSWERS TO CORRESPONDENTS. A.D.D.—Thanks. Arrived while on furlough. R.C. —Yes, 1 quite agree, but hope duties not so strenuous that they will prevent dispatching an occasional communication. "Bessie."—The puzzle referred to is not soluble mathematically, but it can be done by using a little artifice which has confused others also. ' "Colenso."—Much obliged, and it will be looked into at first chance.