POET AND SHERRY.

Evening Post, Issue 2, 2 July 1932, Page 7

POET AND SHERRY.

. A man was given a sum of money topurchase for use at an old boys' reunign a quantity. of port and sherry. Having discretionary power in the transaction he bought the same number of dozens of each kind, all in'the same sized bottles, the port at three pounds per gallon and the sherry;' '•'-, at two pounds, spending in .this : manner the whole s of the money that Was given to him for that purpose. When the goods were being checked with the saleaccounts; the secretary pointed out to "the steward who had made the purchases, that if the total sum of money used in the, purchase had been allotted equally in the two kinds of liquor at the prices stated, instead of buying equal -quantities as he had done, an extra ?tw6 .bpttles^of wine. would, have, been, gained,' 'Can'; the,' reader without the' aid'of'pen. or pencil say hoy, much the; steward' spent '.on 'the-wine'and how many-; bottles* of liquor'Jhe ; would have received < had, the suggestion i.of the secretary been carried out? The win.c was in bottles,-each holding twb-'thirds of a.pint. :' • :,i~ ■■''■:'<-■ ■ ,-t \: -A^BOWEINOK' PARADOX. : The paradox'l concerning bowling averages at. cricket,: hag',cropped up again, in the form.of ;an inquiry by 8.T./' and the ' curious ; position stated by.V the. correspondent ,;shows this perennial 'in an interesting light which is submitted;-for the mental delectation of the reader. Two bowlers," "A" and "B," had -each played in nine matches in :a first-grade competition, and each had obtained. "'■' the", same, average'-of runs per wicket,.being;much •jbettM.'than the; other five player's -who ; w:ers contesting for the bowling trophy. Jn the next; match, the final, '' A -'' not ; only Secured more wickets ,than* V'B^'but his average for that match was a: much better one than his cliibinate'sj; t)'oth being ; then, far ahead, of the others'; in. the competition. The correspondent adds that on the evening of the/match'"AV'-celebratedhis victory ;by, inviting a few friends to dinner,: and the trophy which ■his friends congratulated;; him upon winning was■;shown, at.the.gathering. ;A few days afterwards•*'A',' was astound-: ed to. learn that-"B.'s'' supporters claimed that. thbir v man ■ had.: wpn^thje trophy on the figure's, no dispute being made as to their.accuracy, which are. as follows: At the conclusion, of- the ninth match each.had,,secjired twenty? three wickets-:for one-hundred' 'and', fifteen,runs. In -the next and last, match "A" obtained seven for'siity-1 fire and "B" one.for:seventeen,; Who •won. the trophy^ ..^ ."'■• \ >" ; A DROP XN INOOMEl." ' a .Here' is an interesting little problem suggested by a case recently reported, the facts as revealed being no doubt--simila'r-to the experience of a large number of business people. During the nine years, 1922 to 1930 inclusive, the average, income, of "X." was 12J per cent, greatersthan. it was during the period of junejyears 1923-1931. His income-tax tetuirns^however, show" that the year 1922 was a normal year in which his income was eqnal to the average for the eight years 1923 to 1930. .These are-the facts which came to light when the Income Tax Commissioner disputed the correctness of the return of income which "X" had sent in for the year 1931. Can the reader say how much "X" was due to pay at 6d in the; £ as income tax for that year, with a two hundred pounds exemption, assuming that his income for 1922 was five hundred pounds? Although; this..little: question may not appear at first .glance . to be soluble without the assistance' of pencil and paper, •the, would-bei solver will probably discover upon;examinationthat, the problem is:clearly one for the armchair, as the sender, C.J.W., suggests. WITH A CLUE. Several readers have written to say that the novel problem, '.'A Sum With: out Figures," published recently, was thoroughly enjoyed_, one correspondent calling it a "capital bram-reviver." Here is another one in the form of a long division sum with only six digits and their positions given, the whole of them being "threes." But notwithstanding this clue,', the solver who accomplishes the task of reconstructing the sum.; within; the .space of half an. hour; could not be fairly charged with wasting time. The sum which divides evenly 'without remainder /has four figures-in the divisor, seven/in the dividend, and three in the quotient. Reading from left to right • the digit " three "< is in the fourth position' iii the dividend, another three is in. the first position in the quotient, another in. the last position in the first line of multiplication; yet another in" the: first position in -the first subtraction line, whilst the other two digits of the value mentioned are in the' second line of multiplication, one of them being lathe first position and the other in the third- place. Can. the reader build the complete sum with the aid of the clue given? .. A QTXESTION OP CHANCES. The chances that people, particularly those indulging in sport, are prepared to take when ;the> transaction ,is a ■ financial ono, are not infrequently accepted wit'aout an examination of the mathematical probabilities, and therefore the success of the venture is more or less uncertain. ; But here is a little question on the subject of chances/to be answered ; .mathematically ■ even though the '{ intrepid investor in this class of y transaction may make a success of the."venture":at illogical odds. Three half-sovereigns and a sixpence are placed? upon the table; each- in an opaque envelope of negligibie,;yalue, all of similar;size.and shape,and-with- . out • lany;. distinguishing ■'■■-■ raarks. The question is, what'is the correct amount to pay for permission to draw for keeps" any-one of .the envelopes containing a coin without handling it before purchase? The reader will; of course, note that this little arithmetical Pr°b\ em assumes'v that; when a selection is. made the ratio of the founcpins as indicated.above is maintained,,that IB to. say, the "draw" must be one of four hidden;coins,of the values stated. This should be made an armchair problem even though it^is quite possible to trip the would-be;solver who does not , read the question,carefully. . ■ LAST WEEK'S SOLUTIONS. Expressing 100.—The only example that conforms strictly, to tho conditions IB 3. 69258/714.

A Cricket Match.—' <±" 170 and 3,32 and "Z" 136 and H4 "Diyldlng r £3 4s 2d.—<<A» £1 5s Bd, "B" £1 2s, and "0" 16s 6d. Total £3 4s 2d. ■•■■.■ A Cribbage Ptuszle.— '■■"■■ •' -4- 3 ■■8- ■■• . ■•■ ' : ':';.■■-•. 9 5: i- " ■ .', -.;. .■- ---2 z.;'.6 -. It will be noted that there are nrt "rnns," the score of sixteen beinrf nade up by adding up fifteen in eight

different ways, each of which, in cribbage counts two. , :

The Age of a Tree.- : --The, tree that was first planted was twenty years old at ,the time and the seventeenth four years. Thus the former;was;then four times older than the other or. five timeii as old." ."■ ";.,X; '-.vi ■■■'•- ■: .-■

ANSWERS TO CORRESPONDENTS.

"brigin."^-The': first evidence of mathematics was probably.-, when Eve divided the apple by, two "or, perhaps^ when both she and her spouse found' ,they had five fingers on each hand.

.-, "Alphabetical."—Anything sentV in of the kind mentioned will be,examined if desired, but problems arising in.daily life are those of most;interest. Thanks.

■"■ "Inquirer."—Solutions are not sent by post except in special cases,. but will be mentioned under this heading if they have already appeared as "Intellect Sharpeners." : ' "W"—Thanks, but already published. "Market."—Quite correct as given. "J.A.B."—Somewhat similar. . .

—Quite correct as giyen —Somewhat similar.

Correspondence should be addressed care of P.O. Box/ 1023. .:'•--.