INTELLECT SHARPENERS.

Otago Daily Times, Issue 20586, 8 December 1928, Page 21

INTELLECT SHARPENERS.

By L. Briton. A RESCUE SHIP. - The allocation of the amount of prize .money earned by a rescue ship- which saved a coasting vessel from total loss m a heavy gale last August, and the proportionate distribution of the sum to those manning the ship, provide material for an interesting little problem. The total amount awarded was £IOOO, and one of the questions for the reader to decide is how' the prize money was divided between the captain, three officers, and 36 men who comprised the crew, the conditions of the award being as follows: The captain received four times as much as each officer, and the three officers together were awarded exactly 12 times ag much as each member of the crew of 36, hod if the basis of the allocation was that-. the ..contain received a sum equal to six mo. iris’ salary, and each of the crew a sum equivalent to a month’s pay, what annual salary did each of the three officers receive? Although this embraces two questions, there is only one calculation involved. - ■ NIBBLING A HEDGE. ■Problems concerning “tethered animals” liable to involve calculations in higher, mathematics, and are therefore unsuitable for _ the average newspaper reader, but that variety of “nut" seldom, if ever, finds a place in this column. Here is one, however, that will, require no mental strain to solve, but rather will afford a little recreation .for the brain: A long straight hedge runs along an unused road forming the. boundary of a small property. A donkey is tethered to a peg: on the road exactly eight yards from the hedge. The length of the tether rope is 10 yards, enabling the animal to graze anywhere upto the full length of the line' from the tether post. What length of the hedge will the donkey be able to nibble? The mathematics of this problem prompts the suggestion that the reader should treat it as one to be solved without using pencil or pen. .. . i ANOTHER TETHERED DONKEY. . The paddock in which this donkey was tethered' had only three sides. From one corner the fence Tan in a straight line in a somewhat north-easterly direction, thence direct more or less south-easterly for the; same, as the first-men-tioned fence, the two -termina 1 points being joined by another fence exactly half as long as the other two boundaries together. The paddock contains exactly half an acre, pnd the donkey is tethered to a peg fixed in one of the corners of the enclosure.' The question is what length of tether should be given so that he could, if so desired, graze Over one-half the field only, the assumption being, of courge,' that the animal? could feed to the end of its tether.,- This little poser is not quite as' easy as the previous pne, but it is by no means difficult, while hardly coming within the category of. “armchair problems.” • Anything less than an inch may be ignored. ' • TWO INCOMES.

Two partners in a small city business agreed to draw only a certain proportion of What they were entitled to, and to leave the balance in the business. The amount regularly drawn by the senior partner Jones was greater than the sum taken by Smith, and both partners drew their respective ‘ amounts / uniformly throughout the year, the total sum of the two being £418.195. To find-how much each partner drew would not be possible frbn} this scanty information, but if Jones’s allowance for the year.were reduced 'by -7i per cent., apd Smith’s increased by 7 per cent., both partners would be drawing equal amounts, and this data will no doubt be, ample for the reader to reveal the position. Can he find the respective 'sums? A SQUARE GIRDER. An iron-bark tree-had a perfectly cylindrical:, trunk whose diameter up to 4 heightof more than' 30 feet was 33 inches, the cuoic contents of the trunk so described beifig calculated at 220 cubic feet. A. sawyer bought the 1 tree as r it stood in order to out a square girder from its cylindrical trunk, but, though he obtained one of the maximum dimensions possible, the only profit he made Was by the sale of what he cut off the trunk for firewood when he was making , the girder. Can the, reader find’ '.how -touch the sawyer made if he received at the rate of £3 per cord for the waste' after making the largest square beam possible from the trunk of the contents described, viz., 220 cubic feet having a 33-inch diameter, the ,‘f waste ” mentioned including nothing beyond that part of the tree? This problem 1 will be found to he of a kind that is, frequently met, arid it is very useful to know the methods of calculation. IAST WEEK’S SOLUTIONS. THREE DUTCHMEN AND THEIR ? .wives. ’ ; The three, married couples were: —Capen and Gressell, who bought eight and one turkeys respectively; - Erie (12) and Katrina (9), the third couple being Hans, who purchased 32, and Amund, who bought' 31. ' WITHIN WALKING DISTANCE. The ■ gentleman must have lived exactly twp-thirds of. a mile away from his city * office* ’ * • \ “SANS”,,PEN AND PECIL. The pineapples cost Is 3d each, 3d being gained by selling one for is 6d, and the same,.profit when three are sold in one lot for 4s. AN AVERAGE RATE PER CENT. As Jones’s average gain bn the whole sum in the three enterprises mentioned was 3 per cent., he would neither gain nor lose if the suggested change were effected.' ■ , , .. NOT DIAGONALLY. This is solved,by starting from the same square, No 28 and moving to 29, then to 61, to 64, to 8, to I, to 57, to 58. to 10. Jo 16, to So, to 54. to 22. to 19. to 69' to 6Q, to 28 16 moves being the minimum number undet the conditions stated. ANSWERS TO CORRESPONDENTS. “ Tournament.’’—Thanks. It is an ideal arrangement, as you say, and makes a much more interesting problem. No simply a matter of the ‘ idea ” occur- ( ring. “Poser.”—ln the case quoted it is obvious that nothing could be gained by the purchaser buying more articles than required, though in most instances the principle obtains of “a reduction by taking a quantity.” The calculation is quite good.,