BROTHERS AND SISTERS.

Evening Post, Volume CVIII, Issue 6, 6 July 1929, Page 29

BROTHERS AND SISTERS.

Henry, Max, Owen, and Morvyn each had a sister and the eight engaged in a aeries of competitive games of tennis, .each playing against the other in doublos and singles. There •was a stake, in the games, viz., forty new tennis balls provided by the players in equal. sshares, for as the girls were all in employment and earning good wages,each: scorned the. offer of her brother to subscribe to the "pool" for her,:. They were all 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, Betty's two, ;Joan'a three, while Marie, as waa befitting the eldest, won four balls. Henry won t-be- same number as his sister, while Marie's share was only half as many as her brother won. Owen secured three times the number that his sister won, while for every ball won by Betty her brother won four. This did not, however, exhaust the "pool," the number left over being divided equally between the eight. Can the- reader find the names of Joan's and Betty's brothers? AUGUSTUS ANB CAESAR. Augustus and Caesar working at a survey camp thirty-fivo miles from tho railway station, started off on their bicycles to catch the throe-thirty p.m. train, to the city. After travelling fifteen miles, disaster overtook them for besides a couple of punctures, tha back wheel of one of the machines collapsed, rendering it quite useless. It 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 X'ace. ; Here is a little problem for the reader, viz., to find what method was adopted byT alternatively walking and riding so that both arrived at the railway station together with exactly ten minutes to spare? Their respective rates, of travel woro: Augustus walked at the rate of four miles an hour and rode at ten miles per hour, while Caesar travolled on foot at five miles por hour and on the bicycle at ono mile every seven and a half minutes, both paving tho 20-mile- post at noon. CASHING A CHEQUE. A, cheque of six pounds twelve shillings was presented at one of the city tanks, but the teller when cashing it misread the amount by reversing tho figures, paying out twelve pouuds six shillings. The cheque had boen enclosed in an envelope addressed to tho bank, thus the messenger cashing it was liot able to correct the tellor's mistake. Here is a little problem prompted by the incident: Let it bo supposed that the messenger had been instructed to call at one of the shops in the city to pay an account, and that after doing Uo tho; money he had loft amounted to bxaetly twenty-fonr shillings, less than rtoitblo the amount of the account. Now, assuming that the messenger had no money except the proceeds of tho cheque, can the reader, find with only this information to help him, what was tho amount of the account which the wan paid? This little poser will provide excellent mental exercise if the leader will troat.it as an armchair problem. ' , ' ■ A NOVEL PROBLEM GAME. "Pierrot" has sent the following little- problem game which the reader will find both amusing and instructive, tho latter because it is not governed by chance, a knowledge of the mathematical koy to it ensuring success in every game. Take five squares of a draught board or a diagram of fivo would do equally as well, and number them 1, 2, S, 4, and 5 respectively, in any order. The first player places a counter on any one of them, say two, and calls two, Jus opponent then removing tho counter to another square, say four, counting six, and so on, the player in every case adding the last number of the square played upon to tho total of thoso ijpon which the counter had already Keen placed. The same square must not be plaj-ed upon twice in succession, and the player wins who scores exactly thirty-seven or'forces his opponent >to go beyond that total. Can the reader find the arithmetical key and- make a certainty of winning every time against "a. person not knowing it? A STEP LADDER. 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 stop at a time, so that each tread of. the ladder is stepped upon the same number of times, I wonder how many would give the correct answer at once by stating the method of achievement1? There is no necessity to obtain a stepladder for the purpose of solving this little nut, but try it by diagiam and sco how soon or .how, long it will take to solve it. There is one condition, howevery which makes the question less obvious than it otherwise would be, and that is that the demonstrator must return to the floor once only.