INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20300, 6 July 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

BY T. L. r.RITON.

BROTHERS AND SISTERS.

Henry, Max, Owen and Mervyn, each had a sister, and the eight onguged in a series of competitive games of t«nni», <a.ch playing against the other in doublM and singles. There was a stake in the games, viz.; forty now tennis balls provided by the players in equal shares, for, as tfie girls were all in employment and earning good wages each seorrtMl the offer of her biothcr to subscribe to the " pool " for her. They were ail fairly evenly matched and the games were recorded by points for and against each individual player. The following was the result.—Ethel's share was one ball. Dotty'& two, Joan's three, while Marie, as was befitting the eldest, won four balls Henry won the same number as his sister, while Marie's share was only half us many as her biother won. Owen secured three times the number thai his sister won, whilb for every bull won by Bettv her brother woo four. This did not, however, exhaust the

" pool," the number left. o\ei being divided equally between the eight. Can the reader find the names of Joan's and Hetty's brothers?

AUGUSTUS AND CAESAR. Augustus and Caesar working at A survey camp 35 miles from the railway station, started off on tlicit bicycles U> catch the 3.30 'p.in. Main to the city. After travelling fifteen miles, disaster overtook them for besides a couple of punctures, the buck wheel of one of the machines collapsed, rendering it quite useless. ft was not possible owing to their weight for both men to ride on one machine, so they decided to ride and walk alternatively, not by running beside the bicycle in turns, as one of them was not able to travel On foot beyond a walking pace. The problem is to find what method was adopted bv alternatively walking and riding so that both arrived at the railway station together with exactly ten minutes to spare. Augustus walked at the rate of four miles an hour and rode at ten miles per hour, while Caesar travelled on foot at five miles per hour and on the bicycle at one mile every seven and a half minutes, both leaving the 20 miles post at noon.

CASHING A CHEQUE. A cheque for £6 12s was presented at one of the City batiks, but the teller when cashing it misread the amount by reversing the figures, paying out £l2 6s. The cheque had been enclosed in an envelope <iddies;:ed to the bank, thus, the messen er cashing it was not able to correct the teller's mistake. Let it be supposed that the messenger had been instructed to call at one ot the shops in the city to pay an account, and that after doing so tho money he had left amounted to.exactly 24s less than double the amount of tho account. Now assuming that the messenger had no money except, the proceeds of the cheque can the reader find, with only this information to help him, what was the amount of the account which the man paid ? This w'll provide excellent mental exerciso if the reader will treat it as an armchair problem.

! A NOVEL PROBLEM GAME. " Pierrot" has sent the following problem game which the reader will find btoth amusing and instructive, the latter hecanse it is not governed by chance, » knowledge of the mathematical key to it ensuring success in every game. Take five squares of a draught-hoard or a diagram of five would do equa'lv as well, and number them 1. 2, 3. 4 and 5 respectively, in any order. The first player places a counter on any one of them, say two, and calls two, his opponent then removing the counter to another square, say four, counting six and so on. the player in every case adding the lasfc number of the square played upon to the total of those upon which the counter had _ already been placed. The same square must not be played upon twice in succession, and the player wins who scores exactly 37 or forces his opponent to ro beyond that total. Pan the reader J find the ariflimetical key and make a | certainty of winning every fcimei against a person not knowing it ? A STEP-LADDEM. A step-ladder has ten steps not including the platform at the top, and if the question were asked what is the fewest number of steps necessary to walk twice from the floor to the platform remaining at the top after the second ascent, and taking only one step at a time, so that each tread of the ladder is stepped upou the same number of times, I wonder how many would give the correct answer at once by stating the method of achievement ? There is no necessity to obtain a step-ladder for the purpose of solving this problem, but try it by diagram and seo how soon or how long it will take to solve it. There is one condition, however, which makes the question less obvious than it otherwise would be, and that is that the demonstrator must return to tho floor once only. LAST WEEK'S SOLUTIONS. A Weighing Problem. The weights of the commodities are as follows:—A, 1501b.; B, 81b.; C, 32!b. and D 1101b. A School Committee. It would be possible to vote under the conditions stated in 1,698.159 differed ways. It seems almost incredible with only 23 candidates, but it is- so. k At What Intervals. Always every 65 5-lith minutes, n® matter whether the time piece is running fast, slow or keeping time. A Coincidence. A started with four half-crowns and a shilling; B, with one half-crown, one fiorin, two single shillings and a sixpence, while C had two florins, two sincrle shillings and a sixpence—total, £1 4s 6d. Cutting Up Logs. As there are twice the number in a cord of three feet logs as in a cord of the other sizo. tho price would be one half of 10s for six fee* logs, viz., 5s per cord. But each of the latter requires five cuts to two of She smaller logs, so the correct price per cord for the six feet logs is [2s 6d per cord, or £93 15s for tb6 whoie contract. ANSWERS TO CORRESPONDENTS. J.C.—Thanks—Quite suitable. Seaman. —A " cable length is • hundred fathoms or approximately one tenth of u nautical mile. Metric.—Expressed in pints a Hire il approximately 13 more acrutaleiy 1.7598 pints. S.D.-It is not difficult, but require just a little thought. " Papcrchase." The P n P er dropped every yard was cut into from 24 sheets each lS.m by 22m. Phe 33ft. square re to question intended to be' suhproblem, and was i Xl)irt,v-iri:f stiluted for the fo "". er j 6 utsd ill minutes is the time occup"* «• the solution.