INTELLECT SHARPENERS.

Otago Daily Times, Issue 20086, 30 April 1927, Page 19

INTELLECT SHARPENERS.

By X. L. Beitoit. Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some ot the ‘'nuts” may appear harder than others, it will be found that none will require a sledgehammer to crack it. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. AN ELECTION. Here is a little problem that just now will probably bo found of special interest. Speaking to a friend the other day, a ratepayer of ——, ho said that there was much speculation as to the result of the voting for nine councillors. lit could not su* just then how many nominations then.' would be, as the closing date was some days ahead, but if -ail of the candidates who talked of contesting the election were nominated there would he not fewer than 25 for the nine seats. I thought, then, that these facts would make a capital topical problem for this column. With the figures mentioned, can the reader discover in how many different ways the candidates can bo voted for. assuming that any number not exceeding nine may receive an elector’s vote? It is not a difficult problem, but it is interesting to note the accelerating ratio as the number of councillors voted for increases by steps from one to nine. THE HANDS OF A WATCH Obviously any conditions may be assumed in formulating a problem, provided they are understood and are clearly expressed, in which case the solution of it will always be in accordance with those stipulations or conditions. A clock problem is in mind at the moment, in which the solution may reveal a fact that does not admit of verification in practice, involving a small fractional. part of a second not discernible on the dial. A man took his watch to have it regulated, and stated that there must be something wrong because tl ; io hands came exactly together every job minutes. The watchmaker shook his Wad, indicating that ho was not in agreement with what the man said, but he promised to overhaul the watch. The question then is: At what exact intervals of time do the hands of a watch or any cimepiece coincide or come precisely together? The reader will, of course, see that intervals must bo the’ same whether the watch is running fast or slow, or keeping exact time. A COOK’S DILEMMA. In the party that sat down to dinner at n family reunion there were one grandfather, one grandmother, two fathers, two mothers, four children, throe grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, dug mother-in-law, ami one daughter-in-law. The cool: had asked her mistress the night before how many she would provide for, and was told (hat the party would comprise those mentioned, whereupon she exclaimed. “Lor-a-mcrcy there’s not enough food in tho house for such a lot.” The lady, however, assured her that there would he quite sufficient, hut it was not until nextday when tho cook saw the table being- laid for seven persona only, that she realised that what her mistress had said was correct. Can the reader sav how tho 23 designations mentioned can bo claimed by only seven relatives? FOUR MARRIED COUPLES. Four married couple# from a nearby settlement came into town for the late shopping night. It was necessary for them ■to be economical at they had only four pounds between them. The curious part of the money was that everybody’s sum was made up of florins, and each spent an exact number of these coins, Eliza spending one, Bridget two. Janet three, and Martha four. The husbands, like most men, were, however, more prodigal, for though Hobbs only spent the same amount no his wife, MTnvish, O’Grady, and Miller got rid of twice, three times, and four times as much as their spouses to-peetivolv. U was arranged beforehand that wfiatovcr money was left over should be pooled and divided equally between them, tho number of florins,that were over allowing of their equal division. What were the surnames of each of tho women? AN EXTRAORDINARY NUMBER. I picked up a piece of zinc not long ago on a country road. It had been in two piece*! at one time, and was now laced together in tho form of an oblong, thereby lengthening the pieces. On this was printed the number 9801, but in different colours, the 98 being on one piece in black, and the 01 on the other printed in red. As I carried it along to tho nearest telegraph post to nail it up in a position to bo soon by passers-by, it was observed that (hough neither of the separate numbers could have had any connection originally, being on totally different kinds of zincs, they had something in common. ]t was that tho two added together made 99 which being square made the identical number on tho whole piece, 9801. That night I tried to discover other numbers with this {jocularity, but failed to find more than one in which nil the figures are different as in this. Can the reader discover it, or any other? LAST WEEK’S SOLUTIONS. WINTER FIREWOOD. As both the three and the six feet logs were of tho same thickncs, it is obvious there would be twice as many logs in a cord of the former as tho latter, and f tho same number of outs wore to bo made in one sized log as the other, tho six feet logs would only cost one-half the price of the other—viz., 5s per cord. But the latter logs required only two cuts, whereas each of the eix-fcot timber necessitated five cuts, and therefore, the correct price per cord was 12s 6d. which price the lady willingly paid when the matter was explained. DRAUGHT BOARD LEAP-FROG. The counters being numbered as suggested, the problem can be solved in the manner following:—No. 2 takes 10; No. 4, 12; No. 6,5; No. 3,6; No. 7, 15; No. 8, 16, 7, 14, 3; and lastly No. 1 takes 9,2, 11, 8, 13, and 4 (seven moves). WEIGHING THE FAMILY. The weights were: Father, 1501 b; mother, 1101 b; boy. 321 b; and baby, 81b. A SIMPLE SQUARING UP, At commencement, X had four halfcrowns and a shilling—lls; Y had one half-crown, one florin, two shillings, and one sixpence—7s; and Z had two florins, two shillings, and one sixpence—6s 6d. Total, £1 4s 6d. As X lost 5s and Z lost 6d, the coins each had at the conclusion of the game were, X 'wo florins, one shilling, ami two sixpences—6s. Y had five half-crown*—l2s 6d ; and Z had one florin and four shillings—6s. Total. £1 4s sd. HOW COULD IT BE? Tho amount of tho account was £2, and the gentleman bought a newspaper, leaving £1 19s lOd, thus saving the shopkeeper from stamping tho receipt. Iho Govenimenl lost the twopence. ANSWERS TO CORRESPONDENTS. “Undergraduate.” —Yes, variety as you suggest is one of the features this column endeavours to provide. Thanks for your appreciation and favourable comparison to cro*s-word problems. “F.W.” (Albert Park, Melbourne).Much obliged for your comments, and confirmation of the moving wheel solution Will welcome future notes. “R.C.’’—Replied by post. Tho number is much under-esl imated. I ake a sovereign, for example, which can be tendered In millions of different ways, when the farthing is admitted.