INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20596, 21 June 1930, Page 29 (Supplement)

INTELLECT SHARPENERS.

« BIG " SILVER. 1 ; . KT. & BBIXOX. Four persons, A, By 0, and D, had between them the sum of 16s in silver coins," and though the individual sums were all different, each had the same number of coins. The money was then converted into " big" silver, so that each would possess his sum in the fewest number of silver coins possible, and after this was done they still possessed an equal number, though the total was leS3. The question is to find what actual coins each had in " big" iiilver, the only information avalable being that A's and D's money together equalled that of B and C, that sum comprising as many shillings (in value) as the number of coins the four had between them after conversion into, the highest denominations possible. And if 0 had half as much again as the sum that A had, and one shilling more than B, what amount was possessed by eaehj TIME . AM) DISTANCE. If the reader will make & sketch of a rectangular block of land from the de- ' scripton given, he will readily solve the following interesting and useful problem. The northern boundary A-B, and the southern, D-C, are each seven miles in length, and run from west to cast, the two short boundaries A-D and B-C feeing ' each .five miles, long. There is a boundary line running west to east from E to F, _/hich divides the block yito two sections, the northern one, N, being seven > miles by three, and the southern part, S, seven miles by two. N is all good, solid ground that could bo walked at a rate twice as fast as the southern part which is all loose sand. A man had to walk from .D to B, and although lie knew the character, of the land, took the direct diagonal route between those two points. The question is, that although it is actually the shortest distance, what is the shortest route measured by time from D to B, assuming that a uniform gait is maintained throughout? MORE AMUSING THAN STREHUOUS. Here is a problem solvable by elementary arithmetic or by indeterminate equation, though the reader is recommended to adopt neither method, but to reach the solution by trials—by way of a change—for by doing so, he will probably derive a fuller measure of intellectual amusement. A man bought a number of articles of three different kinds, and at three different prices, spending £l5O in all, purchasing 10 dozen of one kind, 28£ of another (not tiozens) and one-eighth of a dozen 5 of the third variety. What were the respective prices of the three' kinds'Of mer- ' chandise, if on® each of th© three cost £6 Is?IMAGINARY WOOL SALS. Let us lake an imaginary wool sale in - which the raw product was offered in two classes, viz., " scoured " and " greasy," ■ regardless, of grades of qnality, and that two "buying- countries only were represented, which may be called " Bradford " and " Berlin.'" Three times as many bales of scoured: wool-were bought by " Berlin " as the number it rejected, and exactly five times as many of "greasy" were accepted by the German representative. as he refused. Thirteensixteenths. of; the number of bales o£- " scoured *' wool offered to " Bradford " were secured,, but the Yorkshire buyer rejected fosr-fifteenths of the number of bales of "greasy" that were offered to him. Bales of both classes of wool to the num- - ber of 75,400 ivere purchased by the two • agents. The question to decide is, that if the total number of bales of "greasy'* .- v offering was half as many again as the : "scoured," what were the respective number bought by "Bradford" and "Berlin." No bales were offered more than once. " MEETING' OP SHAREHOLDERS. The report of a somewhat tumultuous meeting of shareholders of a commercial. concern recently, when a motion rejecting the directors' proposals was defeated by. a large majority, and afterwards carried by a small -margin, when owing to an irregularity, a fresh vote was taken, suggests a problem. Let it be assumed that in the first division the "noes" were in a majority equal to half the number who > voted that way, everyone present voting : except the chairman, and that before thefresh vote was taken, other shareholders to the number of one less than half a hundred, arrived and voted, resulting-in the " ayes" having a majority of one. The point to. be decided is that as all. those who voted on the first occasion may be assumed to have voted in the same way in the second dvision, how many took part in each vote, everyono present on both occasions voting, except the chairman? LAST WEEK'S SOLUTIONS. Syndicate's Investments, - The sum was £3OO net, the number ,in the syndicate who shared equally being 12. Somewhat Bibulous. The thirsty one started out with 10Jd. Entering hotel No. 3, it is obvious that the man had 6d left, from which It is a simple calculation to find his financial strength at first. Training for Football. Avery would be 1£ miles behind Bates after two hours, their respective rates of travelling being 4} and 5$ miles an hour. Cucumbers and Bananas. The cucumbers dropped from 5s to 4s 2d per hundred, and the bananas were is 3d per dozen. Spider find the Fly. The shortest over the ontside , surface to the top is 15in. and Sin. down the inside, total, Ift. din. It is assumed J . that the pipe bad no geometrical thickness. ANSWERS TO CORRESPONDENTS. " Company."—" Bulls " and " Bears " are, as you state, but " Stag" is a name, in Stock Exchange parlance, for one who makes a practice of applying for shares in a new company with no intention of hold- , ing them. . , , R.A.F.—It was a typographical error, , caused by two lines being transposed. was corrected in the following issue. [ Moutore."—Thanks, but a little too - i intricate for the average reader.