NUTS TO CRACK

Otago Witness, Issue 3972, 29 April 1930, Page 64

NUTS TO CRACK

By

T. L. Briton.

(Foe the Otago Witness.)

Readers with a little Ingenuity will find in this column an abundant store ot 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 ralutions, unless these are specially asked for. but to keep them for comparison with those published in the issue following tho publication of the problems. A SMALL BANKING ACCOUNT. This little account no doubt will be calculated by some readers at first attempt without bothering with pen or pencil, though others may not. In refers to an unknown sum of money which had been left by an uncle to his nephew to be banked for him in five separate amounts on each of his eleventh, twelfth, thir- ! teenth, fourteenth, and fifteenth birthdays respectively. The first deposit was 10 per cent, of the full legacy, the second one-sixth of the balance, the third was double the sum deposited the first time, the fourth being £5O more than the second deposit, whilst the fifth and last was a sum of £l5O, being the residue of the uncle’s gift. How did the boy’s account then stand, assuming there had been no other deposits and no withdrawals, the accumulated interest up to that time Being £34 10s? VAULTING WITH A POLE. The master in charge of the “Activities Club ” of a local college was measuring the heights of several “ vaults ” that had been marked on the upright post during the afternoon, and found Jones’s to be the highest, which was exactly half as high again as the lowest “ vault ” by one of the youngest boys, Smith. When the boys crowded around to ascertain Jones’s record, the sports mastersaid “ this measuring rod is five feet ten inches in length, and when placed upright against the post showing the records, the top of the rod is as far below Jones’s mark as it is above Smith’s.” It was an excellent little mental exercise for the boys after their physical efforts, but it was noted that most of the lads did not attempt to find how high Jones had vaulted until they arrived in the classroom, where they sought the assistance of their slates. Can the reader say without these aids what Jones’s vault was? A CURIOUS PUZZLE. An interesting correspondent (R. C. S.) has sent the following curious puzzle, which he states is based on an idea of a problem (published in a London journal), called “Find the Figures.” the words concerned being “ Saucepan ” and “ kettle.* -■

Here is “ R. C. S’s ” puzzle:— “ The letters in the words ‘ Saturdav and Battle ’ represent the nine digits' and cipher, one for each letter, the ontf figure representing the same letter throughout. Adding together the two' numbers represented by the two words* and then substituting the respective let-’ ters for the figures in the total, it wilt read Isdryuda and if Battle be sub-1 tracted from Saturday by first writing their equivalents in figures, the remainder; when translated to letters, is Beyderr.’f Can the reader find the respective digits and cipher for these 10 letters:— ' This requires no mathmatical skill whatever, but still it will demand the exercise of some ingenuity to solve it’ and the reader with powers of observa J tion and deduction will have an advantage in straightening out the curious puzzle. SHARING THE DAMAGE. Anticipating that possibly the reader’s lead pencil, after being used in the preceding problem, may require •here is a little poser to occupy his mind whilst performing that necessary duty. L A number of boys took a bicycle without permission belonging to an elder brother of one of them, and between the, lot managed to damage it to the extent of five pounds, which all agreed to pay in equal shares. Four of the youngest of them, however, took no actual part in damaging the machine, so the other lads decided to exempt them from any payment. How’ many boys were there altogether if, by exempting four of them, the individual liability of the others totalled four shillings and twopence in excess of what each payment would have been if all had shared equal responsibility? FLOORING A HALL. The scattered settlers in a certain locality built a hall in a convenient centre, quarrying the stone nearby, and perform; ing the whole work of erecting the building’. The flooring of the hall is the subject of this problem, the settlers felling the necessary trees and hauling the logs to a sawmill a few miles away. The miller's payment for the work was 10 per cent, of the quantity sawn, which amounted to exactly’ enough for him tQ floor a shed 20 feet square and a large Toom 20 feet bj’ 10 feet, all the timber being cut in 10-feet lengths. The question is how did the settlers fare for the quantity’ they required for the hall if the floor area was exactly 90 feet by 60 feet? It may be assumed that with the board.-} of the length stated there was no waste by cutting in either case, LAST WEEK'S SOLUTIONS. HOW MANY? There were no horses in the paddock before the pony was put in, so the number is one. TEN CATTIES OF RICE. The coins, when placed on the countei, showed 100, 3,2, 50, 25, 10, 10, 5. 2,1, all representing cents. If the shopkeeper took the first, third, eighth and ninth (109), the customer the fourth, sixth, seventh, and tenth (71), and the third person took the second and the fifth (28), everyone would receive his correct money, and all in different coins to what were held at first. SHORT RUNS. Although five signals were made by the umpires, two were simultaneous, therefore three runs were short. THREE VARIETIES. Seven at 3s per dozen, eight at 2s per dozen, and 14 at Is per dozen, total two dozen and five for 4s 3d. EASTER EGGS. One hundred dozen. ANSWERS TO CORRESPONDENTS. “ Calculus.”—The square of every odd number when divided by 8 leaves a remainder of 1, provided that the dividend exceeds 8. “Metric.”—(l) The British systems are much more difficult for rapid calculation. (2) Thirty-five miles equal 56 kilometres. (3) By set diagram is the quickest method of obtaining British equivalents of metric measures and vice versa. J. E. W.—Next week.

“ Poles.”—The cardinal points at the Poles are limited to one, thus at the South Pole all aspects are north.