INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20454, 4 January 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

ELECTRIC LIGHT. ACCOUNT,

BY T. L. BRITON.

The management, of a country picture theatre always pays local accounts monthly in cash, and on a recent occasion the accountant tendered at the local Power Board office the amount for that month's lighting services in ten shilling notes, halfcrowns and two shilling pieces. The only detail available concerning the numbers or amounts of the respective denominations tendered is that the total sum paid in halfcrowns was the same as that paid in halfnotes ; but, if other data are assumed, the reader will be able to find ->what was the amount of the account. If the ten shilling notes had been half-crowns and the hallcrowns had been half-notes the account would be £ll 16s 6d. If the ten shilling notes had been florins and the florins ten shilling notes the amount would be £9. But if the number of half-crowns and the number of florins were interchanged the amount would be £6. Can the reader find the exact amount of the account, and in what form it was tendered ?

A DEAL IN RAMI3. For the purpose of buying a number of flock and stiicT rams a stock dealer borrowed the purchase money at 10 per cent, on the security oi: the stock bought; the lender having confidence in the dealer's judgment in transactions of this kind, the advance being for the period between purchase and re-sale. Forty-eighb rams were bought at an average price of £3l ss, and at next monthly sales they were quitted .at the following prices.:—Fourteen at £25 each, ten at £2B 2s 6d eachy nine at £4O, and fifteen " studs " at £56 5s each. The month's droving, feed and wages expenses added to insurance premiums were paid out of the dealer's profits after returning the lender his money, plus 10 per cent, on purchase money advanced. Assuming that the costs, exclusive of interest, amounted to £5 less than the net profits of tho transaction, what did the drover make on the deal ?

WALKING "ROUND " A SQUARE. A recreation reserve is exactly 10,000 square yards in area, the block being in the form of a square, and for problem purposes it may _be assumed that although fenced it is possible to walk on the actual boundaries. Two athletes start from opposite corners to walk along the perimeter, both going in the same direction, Jones travelling nineteen yards to every sixteen covered by Hopkins. Assuming that both walk uniformly at these relative speeds, how many times does eacli athlete pass his own starting corner before Jones catches the other, and at what point, measured from either of the two starting points, does he come up to Hopkins ? PARTNERS AND PROFITS. . A man commenced business in a small way, putting £624 into it, and four months afterwards decided to extend the concern, taking in for this purpose a partner who invested £728 in the business. Although b the trade warranted a' further extension the two partners had no available ready money, and both being averse to borrowing it was agreed to admit a third partner, who brought £312 into the'enterprise. The net profits for the first twelve months from the date of the commencement of the business amounted to £316 6s Bd, and as this sum was divided between the three in proportion to the amounts and periods of investments can the reader calculate the respective shares of these profits if the third partner came in two months after the second ?

EXPLAINING THE METHOD. " D.K.D." writes:—" Although lam only sixteen I take a very great interest in your column, and therefore feel justified in venturing a suggestion. I think it would mako your column even more interesting if you published, with solutions, the method of working out the problems given the previous week. I managed to get the altitude of the whale-chaser's mast by drawing a diagram according to your description, but could not make the calculation, and so decided to write for the formula. Even if one problem less were published and its space given to an explanation of methods of working I am sure, it would be very acceptable to many others as well."—To do this in every instance would not be desirable, as it would lessen y the value of the problems as " Intellect Sharpeners," the majority of them not being difficult, but in the case of a " nut " being harder to crack than the ordinary an easy way of reaching its kernel will be shown, and will appear with solutions. The method of calculating the whaler's mast problem has since been published.

LAST WEEK'S SOLUTIONS.

Somewhat Different. There is only one arrangement of this curious puzzle, viz., 715 multiplied by 46. which gives 32,890, thus all digits and ciphers are included.

Question ol Overtime. As each of the eighteen men worked at the same speed, every man put in two hours per day overtime after the extra three men were put on, viz., 10 hours a day.

Family Holiday Trip. The family was able to prolong the trip bv twelve days, the holiday occupying 48 days instead of 36, as originally planned;

A Five Figure Number.

The answer is 36,461, the square numbers being 36.64. 4, 81, 1, also the number itself, and with slightly altered conditions 361 also.

Box and Cox. Tha stream Bowed at the rate of too miles an hour.

ANSWERS TO CORRESPONDENTS

" In doubt." —There should be no waste whatever if tha width of tbo room is an exact multiple of the width of the linoleum, otherwise a portion of the last strip should be cut off from end to end if it is necessary to cover the whole area.

N.S.A.—(I) The ratio which one quantity bears to another depends only on their " magnititudes," not on the " units" in terms of which they are measured. (2) " Boiling point " is the temperature of steam from boiling water, the respective points being 212, 100, 80 degrees by Fahrenheit, Centigrade, and Remur.