INTELLECT SHARPENERS.

Otago Daily Times, Issue 20638, 9 February 1929, Page 22

INTELLECT SHARPENERS.

By T. L. Briton. THE PARTY OF ONE. Concerning the problem entitled “A Unanimous Family Party,” a reader Ims written anticipating the answer 'and stating that his friends all agree that it is "one gentleman only,” yet cannot explain how it is possible under our marriage laws for one man to be “ his fathers brother-in-law, his brother’s father-in-law, his father-in-law’s brother-in-law, and his brother-in-law’s father-in-law.” Well, I here is one perfectly legal way in which it could .happen, and though it may be somewhat unusual, our laws make the position quite possible. Bet ns suppose that Hopkins is this family Pooh-bah, and that he is a widower with one daughter, a brother, and a. sister. Hopkins and his father (also a widower) marry two sisters, the former’s wife having a daughter by her first husband. He was thus his father's brother-in-law. Hopkins’s brother marries the former’s stepdaughter and thereupon becomes his brother’s father-in-law. Hopkins's father-in-law marries the former’s sister and thus became his father-in-law’s brother-in-law, and finally Hopkins’s brother-in-law marries the former’s own daughter and consequently he becomes the father-in-law of the brother-in-law. Perhaps the reader will require a little time to absorb this queer mixture, and for the present it may be left at this stage. BY CAR AND MOTOR BICYCLE. Here is an interesting little problem which, involves a useful and easy calculation. Some readers may perhaps elect to solve it without the aid of pen or pencil A man travels 60 miles, partly by ear, along’ a good road, and partly by motor bicycle over a bush track, but if >t had been practicable and he had gone the whole distance by car at the same uniform speed the journey would have ended one hour sooner, and he would thus have saved two-fifths of the time occupied on the motor bicycle. On the assumption that both machines travelled at uniform rates throughout, and that no time was lost in changing from the car to the twowheeler, how far did the man travel on the latter'machine, the time occupied in travelling the full distance of 60 miles by the vehicles mentioned being three hours'? THREE MEN BAN A RACE. Whilst we are vein of speed problems the following triangular duel ” between three men who ran a race over a distance of one mile will probably serve to stimulate the mental faculties of the solver. The throe competitors started together from scratch, and Jones, who won, beat the_ last man. Brown, by yardsj Robertson, who ran second, beating him by 11 seconds. Now, Jones and Robinson were fairly evenly matched in a longdistance race, their relative speeds in the present bntest being as 45 to 44. These details may appear meagre, but they are unite sufficient to enable the reader to find in what time each of the athletes ran the mile. A solution in an even number of minutes and seconds js all that is required, and if one forty-sixth of a yard be added to the margin between Jones and Brown at the finish, -the answer to the query will come out in this way. It is quite a simple calculation. A CARPENTER’S DILEMMA. Whilst the, problems that appear in this column have for their object mental r .reation, many of them will be found to, be of practical utility besides, and here is one that cornea within that category. It concerns a difficulty experienced by a ca:penter who had to make a square board out of a gable-shaped piece of rimu without any waste whatever. No dimensions are given, the only available information being that the -lo 7er and major part of the hoard was in the form of a square, and that the top line of the square formed the bacae of the isncelos triangle surmounting it; the equal sides of the three-sided portion being shorter than ths sides of the squ»e. There are several ways in whidhtthe object of the carpenter could be nSiieved. but can tlie reader say bow it cani be done if the condition be' added that the original hoard should not be cut into more than three pieces during the process? A SPIDER AND A FLY. A full description of the shortest route along the,walls, ceiling, and floor referred to in the solution published last week is now given for the information of several readers who have asked for it. A correspondent, “ 5.P.,” has pent along an excellent diagram drawn to scale, demonstrating the solution given, but unfortunately space will not permit of its publication. The reader will, however, he able to make one from the following description 1 . The room, ns already stated, is 32 feet long, 12 feet high, and 12 feet wide.’ The spider travelled obliquely along the end wall to a point on the edge of the ceiling 5 feet 3 inches from the corner, thence across the ceiling to a point on the top of the side wall 7 feet from the same corner, thence diagonally down the side wall to a point on the edge of the floor 7 feet from the corner of the opposite end wall, thence across the floor to a point on the edge of the latter wall 5 feet 3 inches from tlie same corner, thence direct to the fly. The respective distances thus walked were 1 foot 3 inches, 8 feet 9 indies, 20 feet. 8 feet 9 inches, and 1 foot 3 inches-—total 49 feet.. If the diagram be made on paper go shaped that it will told up . in the form of a hollow cube illustrating the room, the route described will show a straight line between the spider and the fly, when the sketch is opened out flat.

LAST WEEK’S SOLUTION'S. A UNANIMOUS FAMILY PARTY. The party consisted of one person only—viz., the gentleman himself. THE WRONG DIRECTION. The distance from K to T direct is 25 miles, from K to P 15 miles, and from P——- >to T 20 miles. WRITING “ONE HUNDRED” IN ’ , FIGURES. . (L Under tire conditions stated there is only one way of writing the figures equalling one hundred—viz.-. Ninety nine and ninety-nine ninths. (2) 123 minus 45, minus 67, plus 89. equal one hundred, and the other example using four signs is 123 plus 45, minus 67, plus 8, minus 9. DOLLARS, DIMES, AND CENTS. After completing t lie business the tradesman had a one hundred cent piece, a tliicc cent and two two cent pieces, the purchaser a fifty cent piece, two ten cent ami a on e cent, while the third party had a twenty-five and a Hyec cent piece. THE FLASH OFW GUN. The vessel’s rate of steaming for the short distance described was nearly fourteen feet per second, or to be exact, thirteen point eighty-two.

ANSWERS TO CORRESPONDENTS. “ Fogged,’] —The correct and only solution is £24, but algebra is not required to make the calculation. Try it arithmetically as an ordinary profit and loss problem, “ Mt. Pleasant.”—Yts, quite correct. “Not Diagonally.”—There arc only two n ays in 16 moves starting from square No. 28, but there are many different routes if 17 moves are allowed, commencing at 28. “Euclid.”—At present it is not intended to illustrate this column by diagrams, geometrical or otherwise. “Madeira_ Wine.”—lt is obvious that by omitting the total suu of four gallons of each grade of wine there would be other correct solutions in addition to the one already published. In stating the problem, V4/6 should have been mentioned. “ Colenso ” and “Q. E. D.”—Memos received, with thanks.