NUTS TO CRACK.

Otago Witness, Issue 3881, 31 July 1928, Page 69

NUTS TO CRACK.

By

T. L. Briton.

(For tub Otago Witness.) Readers with a little ingenuity will find In ds column an abundant store of entertainmei' and amusement, and the solving of the problems uhould provide excellent mental exhilaration. While some of the "nuts” may appear harder than ethers, it will be found that none will require a sledge-hammer te crack them. Solutions will appear in our next Inoue together with some fresh nuts.” Readers re requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published in ths issue following the publication of the problems. FAMINE IN CHINA. Although China Jias probably the finest and largest tracts’’of agricultural lands in the world, the inhabitants of other countries are periodically asked to. subscribe to famine relief funds. Recently cabled reports that nearly 1,000,000 were starving in the province of Shantung, devastated by the civil wars, and that* grain was being rushed across from Canada to their aid suggest a little problem. Supposing that the 125,000 bushels of wheat that were landed in Kiaochou Bay were so divided amongst 1,000,000 Chinese that each man •'received 12 quarts, each woman eight quarts, and each child two quarts, how many of each class participated in the distribution ’ There could obviously be more than one way that such a division could be effected, but as the proportion of women to men was five to one, there is only one solution possible. Can the reader find it?

• "‘PLANTING APPLE TREES. Two sons of a farmer were each given exactly one acre of land to make an apple orchard for himself. They could take the land in any shape desired, provided both sections were within the homestead paddock, which had been securely wire-netted, thus obviating the necessity of fencing their blocks. One condition was that the trees on each section should be 20ft apart and in rows. Harry selected his block in the form of a square, while Dick marked his (a few chains distant) in equila-teral-triangular shape, thinking that as the trees could be planted on the actual boundaries which were unfenced, a greater number could be grown on it than on a square block. The two areas were planted accordingly, and every tree on both blocks produced four cases of apples in their first season. Now, supposing that each boy netted two and sixpence per case, who received the larger cheque and by how much? A FEAT. ' The diagram below consisting of an oblong divided into six squares is intended to contain the words “ A Feat.” The letters in the original block were not printed in this way, but were movable, and thus four of them became transposed, viz., the t and capital F, also the a and e as will be seen. Can the reader remedy this under the following conditions and restore the letters to their proper places, leaving the blank space as it is now? The letters may be moved horizontally or perpendicularly to an adjoining vacant square, but may not be moved diagonally, and jumping over a letter will also infringe the conditions. Finally, no letter must be removed from the hoard in the process of solution. Try this with lettered counters, and, the problem being a new one, the sender of the first correct solution in the fewest moves less than 20, will be given the opportunity of enjoy ing an exhilarating brain stimulant on every day of the year, in the form of a first copy of a hook to be published shortly, entitled" Three Hundred and Sixty-five Intellect Sharpeners with Solutions, Formula?, and Methods of Solving.” As this problem has not appeared in print before and readers therefore having had no previous opportunity of examining it, there is every probability of a solution being found in fewer than 20 moves. - - i ~r~ — A| |t I _l I j a I e I F I I UNEQUAL SHARES. A grocer commenced business in a small way putting £624 info it, intending to run the concern himself, with the occasional help of his wife, but it grew so rapidly that at the end of four months he-*had to extend, and took in Jones as a .partner. Jones invested £728 in the business. Later on an outside man was found necessary, and it was .decided to get an employee who would put a little capita) into the concern so that he would have more than a wage-earning interest. Exactly two months after Jones’s entry, Hopkins was employed, and he put in the business £312. If the profits of the establishment at the end of 12 months from ths date.that the grocer started, the business were £316 fa Bd. how should his sum be divided between the three partners? A person can easily be tripped when calculating an ordinary transaction such as this. A RAILWAY PROBLEM. Railway affairs being very much in the public mind just now, here is a little financial question relating to them

which, however, has no concern of figures official. Let us suppose that the capital invested' in the railways amounts to £48,000,000, that in both islands the number of trains that travel over all distances is equal to an aveiage of 50 trains over a given mileage daily, and that each of the 50 S^ r .’ cs i° ad of 100 tons of goods. With this assumption, wliat should be the freight per ton charged for that distance in order that the goods traffic without the passenger business will produce receipts sufficient to pay 4 per cent, per annum upon the capital mentioned, and provide a sinking fund of £120,000, it being conceded that the work can be carried on for 360 days in the year. Though the figures are big, the amount of mental effort required to solve this problem will be found to be small.

LAST WEEK'S SOLUTIONS. IN THE GARDEN OF EDEN. A s the number 82,056 was fixed some years ago, and experts have not been able to increase it, that score will perhaps now stand. SEVENS ALL. , There are 876 different ways that counters can be so arranged that they will count seven o n each side of the square. Of course, this number includes reflections and transpositions as stated in the problem. TWO OARSMEN. The stream must have flowed at the rate of two miles per hour, from which the speed of the oarsmen i s obvious. CHINESE BANK TELLERS. There was £6 4s in the bag, the coins being five half-sovereigns, 20 half-crowns, and 12 florins, this being the only way that the amonnt could "be made up under the stipulated conditions. A SQUARE RECREATION GROUND. A must have passed his starting point three times and B twice past his corner, the former catching up to B at a point 66 2-3 yards from the cc-ner where A started. ANSWERS TO CORRESPONDENTS. R.G.—Yes, every line arrangement will also make one nerfectly spherical, as is easily proved in the manner shown. C.T.R.—Twenty-one would be the cycle number in that case. 'Carterton.” —On June 5 this year.