INTELLECT SHARPENERS

Evening Post, Volume CV, Issue 123, 26 May 1928, Page 20

INTELLECT SHARPENERS

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| (By T. L. Briton.) I

Readers with a little ingenuity will find in this column an abundant store of entertainment and Amusement, and the solving of tlio' problems should provide excellent mental'exhilaration. While some of the "nuts" may appear harder ! than others, it will be found that ] none will require a sledge-hammer to crack them. A GOVERNMENT LOAN. 'The new money received by a certain Dominion which recently floated a five million conversion loan was, according to the cabled reports, £1,658,755, tho balance being absorbed by the: extinction, of a former three million advance, and the usual conversion and interest charges. No other details were given beyond the statement that it was a short-dated loan at 4 per cent., the stock being at par. Assuming that one of the terms of the loan was that the now money received by the borrowing State, together with interest on its outstanding balance, had to be repaid in equal annual instalments, what sum should be paid each year in order that tho cash received would be repaid in four years? V '•• PUZZLING ARRANGEMENT. To solve this apparently simple problem will perhaps tax the reader's ihgenuity more than his astuteness in mathematics, and may also require from him a good measure of patience. Of• course, it is possible to hit on the solution by chance at once, though the probabilities are against it, but in any case the effort to solve it should not lack interest. , Take the individual ton figures in the order written, viz.: 7, 1, 5, 4, 6, 2, 3, 8, 9, •0, and divide them into three groups, each group consisting of .any number of figures desired, so that one group multiplied by another will produce the third. Of course, when, the groups have been selected the figures will be no longer individual, but each group will form one complete quantity, for example, 7, >1, 5 would be seven hundred and fifteen, and so. on. The order of the figures as written should not be disturbed, and. may be treated as circulating, as 0 can come either after or before 9 and 7, for example, 907 and 709 would each be in order. THE SECOND MRS. M'TAVISH. Mr. M'Tavish .hail been twice married, and'on 23rd March, 1928, his wife reminded him that that day was the eighteenth anniversary of- their wedding. While discussing this and kindred subjects it transpired that the combined ages of his late spouse: and that'of- his present wife on their respective wedding days totalled exactly his . own age on the latter occasion, on which day ho was just three times tho age of his newly-wedded life-part-ner. Assuming that when this conversation took place the wife's ago was exactly one-half that of her husband, in what year was the latter born .and hbw old was tho second Mrs. M'Tavish when married ?■' ■ ■ ■" ■ '■•' A TRADESMAN'S STOCK. A tradesman seeking' further capital in his business issued the following statement .of his position:—Stock in trade valued on Ist January, 1927, at' £800, on which date he had in cash £350 and owed £1870. His personal expenses for that year, viz., £300, were paid out of the proceeds of .the business, and on Ist -January, 1928, his slock was valued1 £7950, he had" then £570 in cash and owed: £l'slO. It is an easy and useful problem of a kind met with daily to find what the tradesman's profits were for 1927, after deducting 5 per. cent, on tho assets with which he began that year, but can tho reader determine what per-, eentagc of that income was absorbed by life insurance ■ premiums, if his annual payments under' that: head were £41 ss? ..- • ■ ' ;':' '■ A FOUR BY FOUR SQUARE. Here is- an interesting little poser. Draw a sixteen square and place a couuter on each of three squares in such a way that no counter will bo in a direct line with another, perpendicularly, horizontally, or diagonally, and that every unoccupied square will be in a direct line with a square that contains a counter.. There may appear, to be many different -arrangements to; which these conditions apply, but there are actually only two, and to find them will require some patience. ■ LAST WEEK'S SOLUTIONS. The Totalisator.—lf only the dividends be invested on each of the 2nd,3rd, 4th, sth, 6th, 7th, and Bth races, that is to say, that no new money be speculated on the-machine after the first race, the Government taxation and a club's commission would absorb approximately 72 per cent, of the actual money brought to the racecourse and put on the machine. For example: if the sum of £10,000 be invested on the first race, and only dividends speculated on each subsequent event, the public would be able to go home after the eighth race with nearly £2800 between them out of their £10,000, for. that is all that would be left of it. The legal deductions are based on the: machine's "turnover" and not oil "actual" money, so. that in the oxample now given the 15 per cent, would bo calculated on a sum of approximately £48,000, and not on £10,000, as some readers may have thought; thus practically £7 out of every £10 taken to tho course would™be legally absorbed in "costs." Such a position is quite possible. The Boy and the Nuts.—The boy: spent £10 in the purchase of 58,800 nuts, and made a profit of one penny in the venture. . Easter Railway Tourists.—There must have been 524 intending passengers left on the station. A Contractor's Alternative.—The cost would have been £6000 if the given number of workmen comprised equal numbers from each gang. The Professor's Age.—The professor must be 68 years of age in the year; 1928. . ■ ■ . • .