"NUTS!"

Evening Post, Volume CVII, Issue 32, 9 February 1929, Page 27

"NUTS!"

I INTELLECT SHARPENERS |

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| (By T. /,. Briton.) | i^i iiiiiiiiiiiiiufii'miiiiiiirin

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. of the "nuts" may appear harder than others, it will be found that none will require a sledge-hammer to crack them. THE PARTY. OF ONE.

Concerning the problem entitled "A unanimous family party," a reader lias' written ■ anticipating the answer,- and stating that his friends all:'agreo that it is'"one gentleman only," yet cannot explain how it is possible under our marriage laws for one man to be "his father's 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, here is one perfectly legal way in which it could happen, and, though it may be somewhat unusual, our laws mako the position quite possible. Let us suppose that Hopkins is this family Pooh-bah, ana that; he is a widower with one daugh- , ter, Va 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 tho former's stepdaughter, and thereupon became his brother's father-in-law. 's ' fath6r-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 'a own' daughter and- consequently he became tie 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 bo left at this stage. BY CAR AND MOTOR-CYCLE.

Here is an interesting little problem winch involves a useful and easy calculation, and one which some readers perhaps will elect to make without the aid of pen" or pencil.

A man travels sixty miles partly by car along a good road, and partly by, motor-bicycle over a bush track, but if it 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 thus have saved two-fifths of the time occupied oa the ".motor-bike." Assuming that both machines travelled at uniform rates throughout, and that no time was. lost in changing from the car to the "two wheeler," how far did the. man travel on the latter machine, the time occupied in travelling the" full distance of sixty miles by the vehicles mentioned being three hours. THREE MEN RAN A RACE. ' Whilst in the vein of speed problems the following "triangular duel" between three men who ran a race over a distance of one mile will probably serve 1 to stimulate the mental faculties of tie solver. A

The three competitors started together from scratch and Jones, who won, beat the last man, Brown, by seventy-six and a half yards; Bobertson, who ran second, beating him by eleven seconds. Now Jones and Robertson were fairly evenly matched in a long-distance race, their relative 'speeds in the present contest being as fortylive to forty-four. These details may appear meagre, but they are quite 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 is all that is roquired, and if one forty-sixth of a yard bo added to the margin between-, Jones and Brown at the finish, the answer to the query will come out fii 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 recreation, many of them will be found to be of practical utility besides, and here is one that comes within that category. It concerns a difficulty experienced by a carpenter who had to make a square board out of a gableshaped piece of rimu without any waste whatever. No dimensions-are given, the only available information being that, the lower and major part of the board was in the form of a. square, and that the top line of the square forms the base of the isoceles triangle surmounting it, the equal sides of the three-sided portion being shorter than the 1 sides of the square. There are several ways in which the object of the carpenter could be achieved, but can the reader say how it can be done if the condition bo added that.the original board should not be cut into, more than three pieces during the process? A SPIDEE AND A FLY. A full description of the shortest route along the walls, coiling, and floor, referred to in the solution published last week is now given for the information of soveralreaders who have asked for it. A correspondent, "5.P.,," has sent along an excellent diagram dJtawn to scale, demonstrating the solution given, but unfortunately space will not permit of its publication. The reader will, however, be able to make one from the following description. Theroom,' as already stated, is thirty-two feet long, twelve feet high, and twelve feet wide, the spider travelling ob-

liquoly. along tho ond wall to a point .ontlie-cdgo of.the coiling five feet three inches from the corner, thence across the ceiling to a point on tho top of the sido wall seven feet from the same cornor, thenco diagonally down the siile wall to a point on tho edge of tho floor seven feet from tho corner of tho op' posite end wall, thence across tho floor to a point on the.cdgo of the latter wall fivo feet three inehe.T from tho same corner, thenco direct to the fly—the respective distances thus walked being lft Sin, Bft 9in, 20ft, Bft 9in, and lft 3in— total 40 feet. If the diagram be-^-iade on paper so shaped that it will fold up in the form of a hollow cube illustrating the room, the route described will show* a straight line between tho spider and tho fly, when the sketch is opened out ilat. LAST WEEK'S SOLUTIONS. A Unanimous Family Party.—The party consisted of'one-person only, viz., the gentleman himself. '

The Wrong Direction.'—The distance from X— to T— direct is twenty-five miles, from X— to P —. fifteen miles, and from-P—-to T— twenty miles.

Writing "One Hundred" in Figures. —(1) Under the conditions stated there is only one way of writing the figures equalling one hundred, viz., ninety-nine and ninety-nine ninety-ninths; (2) 123 minus 45 minus 67 plus 89 equal one hundred; and the other example using four signs is 123- plus 4o minus G7 plus 8 minus 9.

Dollars, Dimes,- and Cents.-—After completing the business, the tradesman had a .pne, hundred cent*.;piece,,, a three cent and. two .two cent pieces,' the' purchaser a fifty cent piece, two ten cents, and a one cent, while th& third party had a twenty-five and a three cent piece. ■

The Flash of a Gun. —The vessclis rate of steaming for tho short distance prescribed was nearly fourteen feet per second, or, to be exact, thirteen point eight ,two. Answers to Correspondents. "Mt. Pleasant." —Yes, quite correct. ' ""Forged."—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..

■ "Not Diagonally."—There are only two ways in 16 moves, starting at square No. 28, bul there are many different routes if 17 moves are allowed, commencing at 28.