Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21248, 30 July 1932, Page 5 (Supplement)

Intellect Sharpeners

ONLY TWO EXAMPLES BY T. L. BRITON It is not difficult to arrange the nine digits 1 to 9 in three rows of three each, bo that the figures in the two top rows will, as numbers, form an addition sum adding up to a total as shown in the bottom row. But to construct a square by arranging the nine digits in this way, so that besides having the feature described, the arrangement will bo such that the number represented by one of the rows will be equivalent to exactly one-third tho total of the three, the puzzle is not quite so easy to solve. Aad If anotherstipulation be added to the two conditions mentioned, tho reader should find a question which should give somo hard thinking. The third stipulation is that when the square ia thus formed, the digits comprised in each of the two long diagonals must add up 15. There are. only' two examples 'of the nine digits being arranged '/rith the three conditions mentioned, and as tbere is no formula or rule by which these can be determined, the would-be solver should find material for tho exercise of his ingenuity. GOLD-BUYING PROBLEM The activities in gold-buying hav« prompted a curious weighing puzzle which, however, will bo confined to pure gold in the alluvial state, and in order to make an armchair problem of ifc the price will be fixed at an even £6 an ounce. The accountant of a gold-buy-ing firm, after checking tho invoices con* taining the correct weights of five packets of gold marked respectively J.K.L.M.N., confirmed his figures by weighing the parcels in " twos," each being a different pair. The 10 weights thus found were;— 30, 32, 33, 34, 35, 36, 37, 38, 40 and 41 ounces, tho weights of the paper wrappings being negligible, and from these figures he found the respective weights of the five packets, which all agreed with those in the invoices Although the use of pen or pencil should not be absolutely necessary, they are not barred to the would-be solver in his effort to find the value of each of the pcckets In question, the whole of them, as may be easily deducted from the above information, being of the value of £534. > i SEATING ACCOMMODATION The alphabetically-arranged rows of chairs to be seen in entertainment halls, suggests a problem for the armchair in the form of an arithmetical puzzle using letters instead of figures. There are MS rows of chairs, each; of which contains PA number of individual seats, and at a recent gathering each of the seats was occupied by someone—man, woman or child—the occupants comprising the wholo audience. There were ILIE persons all told, the number of men being represented by the letters RLO, th,e number of women by PPN, and tne number of children by ISA, the number of the latter being exactly one-third that of the men. Women made up M/P of the number of men, and the number hi children- to the number of women was I/M. Had there been one fewer rows and one more seat .in each row the number of seats would be ILLL. A keen • reader of this column, '' Mark/' who has sent these details, asks if any Teader can say without the aid of pen or pencil how many persons were present, the number as stated being equivalent, to the seating accommpdation ? GOLD, SILVER AND COPPER COINS : The present abnormal value of the i sovereign suggests the difference in the . effect of mutilated gold coin and tiiose of either silver or copper similarly treated, , for there is no fixed exchange value of ; silver or copper, any more than there is for any article of merchandise. If we cut a sovereign in halves the nominal value of each part is 10s, less cost of mintage, perhaps, but in the case of ' silver and copper coins, dissection will render them practically valueless. Let us assume, however, that coins_ of the 1 two latter-mentioned metals retain, after 1 mutilation, their intrinsic value as in the 1 case of the sovereign, and that the value of a shilling is one-twentieth of a pound, ' and a penny a twelfth of a shilling. If 1 then we take a shilling, a threepenny • piece and a penny, and break off the ; same part of each, what would be the respective values of each of the ■ parts left, if together they are worth la? > Of course the reader does not need any suggestion that this question is purely one for the armchair. j MUCH-DEBATED QUESTION 1 A reader, " Problem-Lover," has asked [ for the publication of a problem concernI ing the much-debated question # of the possibilities, under natural conditions, of the number of from a single ' animal, and gives the details of an argu--5 ment in the matter between two dairy- ' farmers. Similar questions have ap- ' peared in this column and answered in the 1 prescribed .manner, but as it is always an interesting _ subject, " Problem- > Lover's " request is complied with in the T form of a problem, using his figures a® ; far as possible, in order to make it one • of common interest. What number of I descendants is it possible for a cow 10 [ years of age to have if she has her fir:>t 3 calf at two years of age, and a. calf every year afterwards until the age stated, the "same conditions to apply to all her descendants up to the time that the original cow is 10 years of age ? As the question makes it the "possible" numi bor, the reader will of course take it i for granted that all tho calves a,re heifers; l and that there are not any deaths. LAST WEEK'S SOLUTIONS > Buyers at a Wool Sale.—The largest ' number -of buyers is nine. On the Draught-Board.—Soven mov<« ! is tho fewest possible number. ! Four Married Couples.—Eliza O'Grady, i Bridget Miller, Janet Hobbs and Mary > McTavisli. : For the Armchair.—(l.) 12 x 483 = 5796, and 4 x 1963 > at five, ten at one, and eighty at sixt pence. A Useful Problem. —Fifty rails at 12ft. : each, 600 ft., which is five rails (60ft.) ' less than 10 chains. Forty-nine rails were used and these, enclosed in the manner prescribed, mad<j e.ractly nineteen square yards less .than half an acre in ! area. ) • i ANSWERS TO CORRESPONDENTS i O.J.R-—This issue. ! R.C.—Thanks for interesting letter. 1 J.Y.— Geometrically impossible as one ! crossing must always bo omitted. " Area." —The land connot be divided in the manner suggested to conf °™ 1 the conditions of the testator you quote. .. Mr, trie. "—Hardly suitable without an elaborate diagram/ but the description could -be perhaps put into a form that ' would make an illustration unnecessary. . Thanks. •'Geometry."—Tho surface of the first i you mention contains seven square fee more than the second, th |. JjgS: double that more than the third. It could be simplified.