INTELLECT SHARPENERS.

Otago Daily Times, Issue 20964, 1 March 1930, Page 21

INTELLECT SHARPENERS.

By T, L. Briton. AT A CHURCH BAZAAR. Neither J.ones nor his friend Smith knew what money the other possessed when they entered a hall whore a church bazaar was being held, but they made no secret of the fact that each had 100 silver coins made up of the three lowest new Zealand currencies, no shillings, however, being included in Smith’s money. Rattles and games absorbed ail their money except four shillings, which each had at the finish, the articles won by them being handed in at the stalls to be raffled again. Now if we know how Jones spent his money it will not be difficult to calculate how much each of them started with, the total sum being £7 Os Od. At the first stall Jones spent three shillings more than half he had; at the second he spent half as much as he then had, plus half a sovereign and two threepenny pieces he had received in change; and at the two last stalls he spent two and sixpence more than half of what he had when leaving the second stall. He finished up with a balance of four shillings as stated. How much did each spend and how were Smith’s 100 coins made up if he took with him the least possible number of threepenny pieces? THE LENGTH OF A WALL. A man when erecting a four-foot high stone wall along the boundary of a section, part being then completed, was asked how much farther its length would be, and replied “ Twice as far.” As this did not seem to convey to the questioner exactly what he wanted to know, the mason took a measuring rod 15 feet long and laid it on the top of the wall, one end being level with the end of the stonework. “ There,” he said, “ when the wall is completed it will be longer than this rod by exactly twice as many feet as the rod is now longer than the wall. The rpadcr should note the builder’s two statements carefully, and if he decides to calculate mentally what length the wall would be when finished, he will find the effort much more interesting and instructive than if the calculation is made with the aid of pencil and paper. A SIMPLE PERCENTAGE PROBLEM A capitalist, having a certain sum of money to invest, made a scries of four separate and successive speculations by putting the whole of the available money into each investment. Al Che finish the sum he had was twelve thousand seven hundred and fifty-one pounds four shil-. lings (£12,751 4s), and the problem,is to find with the following particulars how much he had originally. In the first venture he made 5 per cent, on his outlay, and the whole of the money was then invested in another concern which showed a profit of 10 per cent. In the third venture the whole of the money was speculated as before, and this time his profits were 15 per cent. The final investment in which all the money was again placed gave him a gain of 20 per cent. What sum did he have at first? It should be noted that the “ whole of the money ” includes all profits in hand when making an investment. CATCHING A TRAIN. A suburban resident intended to catch a train departing at one minute past noon, and left his house in sufficient time to enable him to arrive at the station at noon. An accident to his car, however, compelled him to take a taxicab at a point one mile from the house. The cab travelled much faster than he had intended in his own car, for, notwithstanding the delay caused by the accident, he arrived at the railway station precisely at noon. Now, if exactly one and a-half hours before the taxi-cab started off with the suburbanite, the time was as many minutes less than half-past 10 o’clock as it was then minuets to noon, at what speed did the cab travel the four miles to the station, assuming that if it had been four furlongs further distant the taxi, at the same rate of travelling, would have arrived there precisely at the time the train was duo to leave—one minute past noon? AN ENDLESS CHAIN. A problem some time ago concernin'* the most economical method to pursue in restoring a broken chain to its original condition, brought forth quite a number of responses from readers who thought that they could improve on the solution, but none of the more economical methods sent in complied with the conditions of the problem. Here is an excellent one of the kind forwarded by J.H.C., who states that “ Sam ” Lloyd is its author. An endless steel chain of 50 links became broken into nine separate pieces. The whole of them were closed links, the others being lost, amf the nine fragments had 3, 4, 5,5, 0,6, 0. 7 and 8 links respectively. It cost threepence each to open a link and sixpence to weld, and the question is whether it would ho cheaper to buy a new endless chain for six shillings and sixpence, or get the nine fragrac’-ts of chain with their 50 closed links made into an endless chain as before. It l is quite a good problem and a little more difficult than the ordinary one of this kind, the solution of it not being us obvious as it may look, and vide the reader with excellent mental exercise, especially as there are several different ways of mending the '-Lain, LAST WEEK’S SOLUTIONS. STATE LOANS. The correspondent correctly states Lne annual interest return as £5" 7s IJcl per cent, per annum on an investment of £9B. The nominal value is £IOO, which means that at the end of live years the investor will receive an additional £2. The difference between £5 145.4 d and £5 7a Ifd represents the annual value, for the period of the loan, of the additional payable on redemption. It- is the practice to quote interest return in tliis way (including redemption) so that a prospective investor may compare witli other investments. “ I FOUND IT.” I. f. d. n. o. If.d.n. o. I. f. u - *• «• t. i. u. n. d. It is not possible in less than 23 moves. THE COST OF TWO_ TICKETS. They started with ss, lost Is, and spent 4 S on two tickets, which therefore cost Cd each more than intended. If Is had been found instead of lost, another ticket at 2s could have been bought. THE MYSTERY OF FIGURES. £CG Gs Od (15918 pence) the digits in each ease adding up to 24. There is no other example under £IO,OOO. A SPEED PROBLEM. June was exactly 25 miles from Nana at five minutes to noon, and at 10 minutes past 11 the cars were' 30 miles apart. TO CORRESPONDENTS. Q. E. D.” See issue of February 15. “ Figures.”—There could bo two, either “ six ” or “ fourteen,” as these numbers both comply with the conditions mentioned. Examine it again and limit to one solution, otherwise it will not be much use, though tlie subject is interestin'*. “ Counters.”—Will appear shortly. ° TWO TOUGH NUTS. The answer to No. 1 is “Bod,” but so far no satisfactory solution of No. 2 has been received.