Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21326, 29 October 1932, Page 5 (Supplement)

Intellect Sharpeners

ARMCHAIR PROBLEMS BY T. L. BRITON The whole oi this week's problems are those which can without undue mental strain be answered from the armchair; but, of course, if more enjoyment can be obtained by using a pencil there is no reason why that aid should not be invoked. I bought threu golf balls all at different prices, spending four shillings in their purchase. The price of one of the balls was exactly one-half- of the other two together, though it was not the cheapest of the three, and if the difference in the prices of those two was two-sevenths of the cost of the lowest-priced ball what did I give fo r them respectively ? The four innings in a cricket match produced 330 rtns, none reaching the century. Team "A " made the highest total of the four innings in their first attempt, and one-third fewer runs in their second. Team " B " scored eleven more in their first innings than they managed to get on their second visit to the batting creases, and thii match resulted in a "tie." If two-icni.fgs-totals taken at random produced 154 runs, what were the scores of both teams respectively ? TRANSACTIONS IN EGGS Ihat two well-known marketing terms have distinct meanings in commerce is indicated by the different prices. A housewife bought a quantity of " newlylaid " eggs at Is 6d a dozen, and the same number of " fresh " one 3 at a much reduced figure, namely Is a dozen, spending in that way all the money she had taken with her. Had she spent half that sum on each kind of eggs the housewife would have obtained two more than she received by purchasing in the manner stated. How much did she spend? Upon another visit to the same shop on' next marketing day she asked for 2 S worth of ' black hens' eggs," and the unsuspecting dealer allowed her to pick them herself. Seeing that the lady had selected the largest he charged her an extra threepence, though she had taken the correct number for her 2s at the price marked up. 1 he question is if the extra price charged meant an increase of 2d a dozen how much a dozen did she pay for them ? HIDDEN WORD NO. 2 The mystery of the " hidden word "■ puzzle published recently " floored " a number of readers, who, however, have expressed their appreciation of this kind of problem. This type has certain advantages over its elderly cousin " Crosswords," not the least being that it is less ponderous and does not require an application of wet towels to the head before reaching a solution. Here is another which in like manner to No. 1 may not involve tedious searching of that useful but not entertaining assistant, a dictionary. The hidden word in the present puzzle consists of nine letters and is to some people as commonly known and used as the words "New Zealanders." As in the first problem of the kind each letter in the order of spelling is represented by a digit, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the clues are 2, 6, 8, a contrivance for raising weights; 4, 1, 7, 9, cultivated in the garden; and 9, 5, 7, 3, 9, an article of dress. The whole word is more often heard in Africa than elsewhere, and iijay be found in the cheapest kind of English dictionary. ■ - / - BUYING FAT LAMBS The following question may. appear to be quite a simple one, bijt probably th® reader will find that it will require a few moments of serious thought, though being a problem to be answered without the use of pen or pencil, the calculation is of the simplest kind. A dealer bought a number of fat lambs for which he paid £6O. He let sundry friends have 15 of them at cqst price, making ho profit whatever on them, but the balance he sold for £54, which showed a profit of 2s a '■ head. The question is how many, lambs did the dealer buy, and how : did the whole transaction result financially- to him ? The profit' of" 2s -a head that." he made when he received £54 is not the average for the number bought, but refers to the balance after deducting 15. J , QUESTION OP AGES F.S. has sent the following problem that may well find a place in this week's column " All for the armchair." " Z " h a native of the city " X," and after an absence from his home town for a certain period of time returned to-day to again make "X " his place of abode. Among his former friends who had remained in "X " —were •"** A " and his daughter " B," and also " C " and his sister " D," and the problem evolved by F.S. concerns the years of those four people now as compared with their respective ages on the day that " Z " left. When he departed from "X " his old school chum "A" was four times as old as " C," and " B " was then three times as old as " D." The position to-day is that "A " is only three times as old as " C," and " B " only twice as old as " D." From this information the reader will quickly note that " A's" present age must be equal to the sum of the other three, and that being so the question which places this problem in the category of those for the armchair is that if after the lapse of a period from to-day, equal in length to the time that "Z" was away, the age of " A " will be fourteen years less than the combined ages of the other three, how old are the four people respectively to-day 1 LAST WEEK'S SOLUTIONS Two for the Armchair.—(l) Five dozen.(2) Nineteen minutes. Ship's Close Call. —The steamer would have maintained an average speed of 12£ miles an hour to enable the 600 miles to be covered before the vessel-began to settle down under the conditions stated. Demonstration or Formula.—There are 13 different ways that it can be done, and it may surprise the reader to know that if the number concerned be doubled, the different ways would be over 400.000. A Problem.—'The feat cannot be accomplished in fewer than 23 moves perpendicularly or horizontally one space only, but if diagonal, moves are allowed it could be done in fewer. A, p, 1, b, r; A, p, 1, b, r; A, p, o, m, e; A, p, o, m, e, o, b, ]; is the simplest. Three Young Sportsi—" A " a florin and two threepenny pieces; " B," two sixpences and a threepenny piece and " 0 " a half-crjgvn, a shilling and a threepenny piece, total 7s 6d. The pitfall that was liable to trip one was that one of the exchanges concerned coins of similar value to satisfy the conditions.

ANSWERS TO CORRESPONDENTS < " " Curious."—Much obliged. W.G.R.—Soe issue of October 1.. , " Mark!"— Much obliged. Will be u' ed later on. - W.H.M. —Thanks, but solutions are limited to the expressed terms of problems, which in this case stated, " none over at last division," the sixth. "■ Credentials."—The selection in Hie case mentioned is obvious, i>ut of course the matter requires some thought when it comes to making the correct division of shares. (2) The theory seems feasible, but will require some examination before giving an opinion. Thanks. - I