NUTS TO CRACK

Otago Witness, Issue 4030, 9 June 1931, Page 5

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 th. ’* nuts " may appear harder than others, it will be found that none will require a sledge-hammer to crack them Solutions will appear tn 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 A CRYPTOGRAPH. Quite a number of readers have written to say how much a cryptograph is enjoyed. These interesting problems certainly imply a challenge to the intellect, and this, coupled with the not uncommon desire to discover a secret, makes them attractive, particularly to the fair sex. Here is one formed from a paragrapj taken from the literary pages of this paper, and it may prove sufficiently ob scure to test the ingenuity of the reader. Every word contains the same number of letters as the original and the punctuation remains unaltered. BCIWFB XZWEYZBUEFI. DRF RFULT OFMYFUIF ZA BCIWFB XZWEYZBUEFI DC BFMMU, CAF YFIJWD CQ DRF GCYWO GZOF OFXYFIIZCA Z 1 UQQFMDZAE DRF RFOVUH YFLFAJFI. SZAE ZPA lUJO RUI DRFYFQCYF CYOFYFO XYCXUEUAOU PT QZWBI DC IRCG DRF GCAOFYI CQ BFMMU, ZAMWJOZAE DRF, XYCXRFDI EYULF, DC UDDYUMD DRF QUZDRQJW QYCB UWW XUYDI CQ DRF GCYWO.

A MUTILATED NUMBER PLATE. A number plate which had been removed from a motor car had been mutilated to the extent that the last Of the five figures had been cut off and welded to the front of the other four, these being 3 0 2 5 in that order. A curious feature about that number is that if the two first figures, 30, be added to the other two, 25, and the total squared, the result would be the original number, 3025. This is not the only four-figure number that possesses similar features, and the question for the reader is to find another. 2 0 2 5 is one, but in that case one >»f the digits is repeated, which renders it not on “ all-fours ” with the example given. Mr Dudeney has arranged a formula to enable similar four-figure numbers to be determined, but it is some what intricate for the average reader, especially when a non-significant nought to the left must be included. But in any case much more amusement may be found in an effort to discover by trial one example of a legitimate number of four figures that possesses the curious features mentioned. Of course, the nought may be used when it is placed in a position of numerical value. MEASURING THREE GALLONS. A dary farmer was conveying two full 10-gallon vessels of milk in the city when he was met on the road by two retailers who each desired to purchase three gallons. The farmer had no measures with him, and no cans of any kind except those containing the 20 gallons of milk, and the only vessels possessed by the retailers were an empty fourgallon can, and a five-gallon one, also empty, as they had expected to obtain the milk at the farm where it could be quickly measured. The sale was effected on the road and between the three men it was completed to the satisfaction of all parties in the fewest number of pourings from one to another of the three vessels mentioned. If the time occupied in one pouring operation was exactly 45 seconds, and each of them took a similar time without any perceptible delay between them, can the reader say how long it took to effect the transfer from the 10-gallon vessels, each retailer receiving his three gallons as stated? AN UNEXPECTED HAPPENING. Twins, a boy and a girl, were born a few weeks after the death of the father, who had made provision in his will for the widow and an expected offspring, but omitted to include the possibility of twins. The terms of the will were that two-thirds of the estate were to be settled upon the child in the event of its being a boy, and one-tliird to the widow. ’ If, however, the new. arrival were a. girl the. mother was to receive two-thirds of the estate and the daughter one-third. The unexpected having happened, a friendly suit was brought into court for the purpose of obtaining a ruling as to the allocation of the property. As the judgment of the court was strictly in accordance with the spirit of the will, and equitable to all parties, can the reader say how the estate was divided? This little question involves more than the simple arithmetical calculation to determine the respective alloca tions, for, although a judge may not give reasons for his judgments, in this case he laid down the grounds for his interpretation of the will. Before making a calculation, therefore, the reader should consider the method of fairly dividing the estate : between the three

according to the terms expressed by the testator.

SIX PENS. Six pens of equal size make up the whole area of an enclosure three chains by two, three of the pens being bounded on the north by a long side of the yard with three along the south boundary. From the top left-hand corner the pens are numbered 1,2, 3,4, 5,6, readin" from left to right, and from each there is a gate leading to the adjoining pen, but no access is provided between the pens at any corner. Thus four gates arc situated in the hurdles running north and south, and three in those running east and west, the outside boundaries of the large enclosure being without openings. Pens 1,2, 3. 4 and a S n°n d i- 1 be J ° r ccu P ied by five rams, A, B, C. D. and E respectivelv, but four managed to get into their wrong compartments, C being in No. 2, B in No. 3, . in No. 4, and Din No. 5. A was in his proper place, while the sixth pen is empty. The problem is to transfer the rains to their proper pens, through the gateways, in fewer than 17 moves, no two animals to occupy the same pen together. 1 ANSWERS TO CORRESPONDENTS. “ Student.(l) The par of exchange then was nominally 25 to the pound, but more accurately 25.221 (2) Foreign bills of exchange between one country and another are used to obviate the necessity of sending large quantities of gold and silver. “ Whakarewarewa.”— Perhaps vou would advise the writer in the’ event of any of your prodigies solving the seven” problem prior to the publication of solution. A.B.C.—It was published on the same day.

SOLUTIONS OF LAST WEEK’S PROBLEMS. FOXES AND GEESE. The exchanges can tie made in five moves for each. Fox F to B, Goose II to C, Fox E to A, Goose G to D, Fox B to H, Goose D to E, Fox A to D Goose C to B, Fox D to G, Goose B to F*. WITH FOUR FIGURES. 15 by 93, 21 by 87, 35 by 41, also 351 by 9. THREE PIECES OF GOLD PLATE. The three diameters form a right-angle triangle as stated, so as the two smaller plates are equal to the larger, “ A ’’ and “B,” each take half of the latter. Place the smallest piece on top of the next in size, concentrically, and mark round the former circumference; it will be seen that the smaller piece of the two plus half the rim of the other will make the third equal share, and the remainder the fouitli. Thus five pieces only are necessary. PARTNERS. . £5OO. -'. .■ ’ ELECTION FIGURES. 107 249 356