NUTS TO CRACK

Otago Witness, Issue 3899, 4 December 1928, Page 17

NUTS TO CRACK

By

T. L. Briton.

(Fob the Otago Witness.)

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. Solutions will appear in our next issue, together with some fresh “ nuts." Readers are requested not to send in their solutions, unless these are specially asked for. but to keep them for comparison with those published in the issue following the publication of the problems. THREE DUTCHMEN AND THEIR WIVES. A correspondent lias sent alon" a problem called “ Three Dutchmen’s Mixes, and asks if it could be published as he and his friends are not in agreement as to the correct solution. It is a good old problem that will probably always be fresh, and will perhaps give the reader of to-day as much thinking as the little poser demanded from his grandfather when tackling it 50 years ago. Three Dutchmen—Hans, Eric and Copen and their wives purchased some turkeys. Each bought as many as he or she gave shillings for one, each of the men paying altogether three pounds three shillings more than his own wife. Hans bought 23 more than and Eric 11 more than Gressel, and -he problem is to discover from these meagre details the name of each Dutchman’s wife, one being called Katrina, another Gressel, and the third Around’ The mathematical part of this little nut is quite interesting, involving a variety of squares and factors, and the leadei will no doubt enjoy the unravelling of the tangle.

WITHIN WALKING DISTANCE. A city lawyer lived in a suburb within walking distance of his office, and it was only on very exceptional occasions that he took a car or other conveyance on his daily visits to the city. He was an adept walker, and could accurately judge his pace, no matter at what rate he travelled. For instance, if he left home at a certain time in the and walked by the usual direct route at five miles an hour, he would reach his office invariably at two minutes to nine o clock, but if he left at the- same time and maintained a uniform rate of three and a third miles an hour his time of arrival would be four minutes later. On the assumption that he always walked the same distance irrespective of any variation in rate, how far is it from his home to the city office? Perhaps most readers will accept this little problem as one to be solved without pen or pencil. If so the enjoyment will be considerably increased. SANS PEN AND PENCIL. Those readers who managed to solve the preceding little problem mentally will scorn any suggestion that inis one should be treated in any other waj even if if be a fact that they are liable to be “ caught ” with it. A fruiterer had a quantity of pineapples for sale, and as they were of equal size and rather small he fixed the price of the lot at one and sixpence each, or three for four shillings. He quitted the whole of the consignment at these rates. The question for the reader to answer is: What did the pineapples each cost him if he only made the same profit by the sale of three in a lot as he made on the sale of one at the prices mentioned?

AN AVERAGE RATE PER CENT. Questions relating to averages have a curious knack of frequently tripping up a would-be solver, for very often the correct solution Is not what it appears to be. Here is one, however, that does not present any perplexing difficulties, as it is of a kind met almost daily and of practical utility. Jones has a certain sum of money invested in three securities. One-third of th- total amount produces interest at the rate of 3 per cent, per annum. Upon one-fifth of it, however, he loses 4 per cent, per annum, while the balance of the investment yields a yearly profit of 6 per cent. Jones is now seriously discussing a proposal to place both the second and third mentioned sums in the other security upon which, as stated, he gains 3 per cent. .What rate per cent, would he gain or lose by this re-invest-ment as compared with the average rate per cent, he is now getting on the whole sum? It is quite possible that some readers will decide upon tackling this little “ nut ” while sitting in their armchairs, and if they are successful by mental effort only it will be a meritorious achievement. NOT DIAGONALLY. Here is a little draught board problem that will require quite a lot of patience to enable the correct solution to be arrived at. Place a counter on any one of the 64 squares and try to discover the fewest number of “moves” that are required to “visit every square on the board once, and only once. The conditions are that the counter shall be moved either in a horizontal or vertical direction, but not diagonally, a square being

deemed to have been visited whether it is made a stopping place or passed over. The counter must start and finish at the same square, this being the only exception to the stipulation that a square must not be “ visited ” twice. One “ move ” may include any number of squares provided such move is in the same direction. There are only two possible minimum solutions, one being as follows:—With a board numbered 1 to 64 and reading horizontally from the top left hand corner, commence at square 28 then to 31, to 55, to 50, to 10, to 16, to 8, to 1, to 57, to 64, to 24, t< 19, to 43, to 46, to 38, to 36, to 28 What is the other solution?

LAST WEEK’S SOLUTIONS. TWO MINING PROSPECTORS. Ben walked at the rate of four and a-half miles an hour, and Jim at three miles per hour, the latter travelling 100 miles while Ben covered a total distance of 200 miles. THAT WELL. “Digger” has followed up his first query by stating that he has found the well to be 27 feet deep and not 36 feet, as he thought. ADA; As there are eight letters that can be used to commence the words and only seven to finish them, there must be 56 different ways of writing it. “ Waihi’s “ estimate can therefore not be improved upon. THE CAPACITY OF A TANK. The capacity of the tank is 600 gallons. A GAME OF DOMINOES. The three players must have had two shillings between them at starting, A having Is Id, B 7d, and C 4d, each having 8d at the finish of the three games. ANSWERS TO CORRESPONDENTS. R- C.— (1) On your statement of the position the wine in the small.glass was three-elevenths of the total liquid. (2) An occasional one.

“ Paradox.”—There are several methods of solving the puzzle, but it is, obvious that there is very little differciice between them. It should, however, adopted, the calculation should be made be borne in mind that, w'hichever method is adopted, the calculation should be made with the pivot number always an. odd one.