Intellect Sharpeners.

New Zealand Herald, Volume LXIX, Issue 21224, 2 July 1932, Page 5 (Supplement)

Intellect Sharpeners.

WITH A CLUE.:

BY T. L. BRtTOM.

Several readers have written to saf that the novel problem, " A Sum Without Figures," published recently, was thoroughly enjoyed, one correspondent calling it a " capital brain-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 o! : reconstructing the sum within the space of half-an-hour cciuld not bo 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 tho quotient. Reading from left to right, tho digit " three " is in the fourth position in the dividend, another '* throo "■ ' is i'j the first position in ' the quotient, another in the last position in th,. first line of multiplication, yet another in the first position in tha first subtraction line, while the other two digits of tho value mentioned are in tho second line of multiplication, one of them being in Iho first position and tho other in tho third place Can tho reader build tho completo sum with tho aid of the clue given ? A DROP IN INCOME. Here is an interesting problem, snggosted by a case recently reported, the facts as revealed being, no doubt, similar (o the experience of a large number of business people. During the nine years 1922 to 1930, inclusive, tho averago income of " X " was 12J, per cent, greater than it was during the period of nine years, 1923-1931. His income tax returns, however, show that tho year 1922 was a normal year, in which" his income was equal to the average for the eight years 1923 to 1930. Theso are the facts which came to light when the Income Tax Commissioner disputed the correctness of the return of income which "X " had made for the year 1931. Can the reader say how much " X " was due to pay at 6d in the £ a:s income tax for that year, with a £2OO exemption, assuming that, his income for 1922 was £SOO. Although this question may not appear at first glanco to be soluble without the assistanco of pencil and paper, the would-be solver will probably discover upon that the problem is clearly one for tht. armchair. A BOWLING PARADOX. Tho paradox concerning bowling averages at cricket has cropped up again in the form of an inquiry by 8.T., and the curious position stated by the correspondent shows this perennial in an interesting light. 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 wickot, being much better than the other five players who were contesting for the bowling trophy. In the next match, tho final, " A " not only secured more wickets than " B," but his average for that match was a much better one than his club mate's, both being then far ahead of the other competitors. A few days afterwards " A " was astounded to learn that " B's " supporters claimed that their man had won the trophy on the figures, no dispute being made as to their accuracy, which are as follow At tho conclusion of the ninth match each had secured 23 wickets for 115 runs. In the next and last match " A " obtained seven for 65 and "B " one for 17. Who won tho trophy ? A QUESTION OF CHANCES. Tho chances that peopJo, particularly those indulging in sport, aro prepared to take when the transaction is a financial one, are not infrequently accepted without an examination of tho mathematical probabilities, and therefore the success of the venture is more or less uncertain. Here is a question on tho subject of chances to be answered mathematically, _ even though the intrepid investor in this class of transaction may make a success of the '- venture " at illogical odds. .Three halfsovereigns and a sixpence are placed upon tho table, each in an opaque envelope of negligible) value, all of similar size and shape, and without any distinguishing marks. The question is, what is the correct amount to pay (or 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 arithmetical problem assumes that when a selection is made, the ratio of the four coins, as indicated above, is maintained; that is to say, tho " draw " must be one of four hidden coins of the value«i 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. PORT AND SHERRY. A • V A man was given a sum of money to purchase, for use at a reunion, a quantity of port and sherry n© bought thj> samo number of dozens of each kind, all in tho same-sized' bottles,, tho port, at £3 a gallon and tho sherry at £2, spending in this manner all the money given to him lor that purpose. When -the goods wero being checked with the Bale accounts, the secretary pointed out to the steward, who had mado the purchases, thai; if tho total sum 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 two bottles of wine would have been gained. Can the reader, without tho aid of pen or pencil, say how much tho steward spent on the wine, and how many bottles of liquor ho would have received had the suggestion of tho secretary been carried out? The wine was in "baby" bottles, each holding two-thirds of a pint.

LAST WEEK'S SOLUTIONS. Cricket Match.—" X." 170 and 132, and " Z," 136 and 144. Dividing £3 4s 2d.—" A " £1 5s Bd, "B " £1 :>s, and "C " 16s 6d. Total, £3 4s 2d, Expressing 100.—The only example that conforms strictly to tho conditions it 3.69258/714. Oribbage Puzzle 4 3 6; 9 5 1 2 7 6 It will bo noted in connection with this puzzlo that there are no " runs," tho scoro of 16 being mado up by adding up 15 in eight different ways, each of which in ci'ibbage counts, two. ANSWERS TO CORRESPONDENTS. J.A.B.—Somewhat similar. " Market."—Quite correct as given. " W."—Thanks, but already published. " Alphabetical."—Anything sent 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." " Origin."—The first evidence of mathematics was probably when Eve divided tho apple by two, or,-perhaps, when both she and her spouse found they had fiva fingers on each hand.