COME ONE, COME ALL!

New Zealand Listener, Volume 1, Issue 25, 15 December 1939, Page 55

COME ONE, COME ALL!

UT of the far corners of New Zealand puzzles have been flying in to confound The Listener staff. Readers have taken up the challenge and, we hope, will not lightly let go the advantage gained by cramming the puzzle pigeon hole with packet , after packet of problems and posers of all sorts. So far, we have not done so badly. If we are stumped, we shall probably not admit it, for it is our privilege and relief to hand these worries over to readers in the wicked hope that they will "foam at the mouth and stick straws in their hair," as one correspondent admitted in a reproachful but avenging letter. Come one, come all, there’s an answer somewhere. We like Llewellyn Etherington, of Auckland, for he supplied his own answers to the set printed in our issue of November 24: Answers "It is only fair when problems are set, to give their solutions. The answers to the puzzles I sent in to your issue of November 24 are as follow: "A ton of half-sovereigns is almost a ton of gold; a half-ton of sovereigns is only about half a ton of gold. "The dishonest purchaser of a shirt made a profit of one pound (the shirt and twelve shillings change), so the loss borne by the shopkeeper was the same, one pound. "In the problem of the teacher and the student, the teacher had no cause of action, as the lawyers term it; he could not sue until the terms of the contract were fulfilled, until the student had won a case; he had no legal base for filing a plaint in Court.

"The policeman said that the colour of the dise on his back was white. He reasoned thus: ‘If I have a black disc on my back then B will at once know that he, B, cannot also have a black disc, for in that case C, and only C, will at once see two black discs and know that he cannot have a black disc on his back, for there are only two black discs. C could reason in the same way.’ The test was quite fair for each of them. "As for the problem of the monkey and the weight, I do not know the answer: has it not stumped the editorial staff also? It was originally gasked by Lewis Carroll-the Rev. C. L. Dodgson — when, as a don of Christ Church College, Oxford, he propounded it to the learned men there. He says the Professors of Physics and, I think Mathematics, gave quite different answers. I should think the simplest way would be to try the ‘solvitur ambulando’ test, that is, rig up a rope, borrow a monkey from the Zoo, or a schoolboy, and sive it by actual experiment." Mr. Etherington’s letter partly answers the one from Ruth Collins, of Christchurch, who sent some

answers and will be able to compare hers with the official versions, Apropos of monkeys and weights, she writes: Complications "Puzzles about monkeys and ropes always have me foaming at the mouth and sticking straws in my hair before many minutes have passed, but to my mind this one is unsolvable except by taking the weight of the rope and friction into consideration, Otherwise, equilibrium would be maintained only if the monkey glided up the rope without any jerks or impulses at all. The actual position of the monkey on the rope, in relation to the pulley, does not affect the equilibrium, as unlike levers, etc., the effect of a weight over a pulley does not vary with the distance from the pulley. (Unless I have completely for-

fotten my elementary Physics.) It will be the impetus given to the rope by the monkey’s movements which will set the apparatus in motion, and once in motion, friction and the weight of the rope will affect the situation," And that seems to be a fair statement of a nasty bit of work. But Miss Collins is not content. She liquidated one worry, but supplies another. Here is a sample from her selection of horrors: -And a Relapse Follows A long rope is passed over a pulley. It has a weight at one end and a monkey at the other. There is the same length of rope on either side, and equilibrium is maintained. The rope weighs 4 ozs. per foot. The age of the monkey and the age of the monkey’s mother together total 4 years. The weight of the monkey is as many pounds as the monkey’s mother is years old. The monkey’s monkey’s mother was when the monwas when the monkey’s mother was half as old as, the monkey will be when the monkey is three times as old as the monkey’s mother was when the monkey’s mother was three times as old as the monkey. The weight of the rope and the Weight at the end is half as much again as the difference in weight between the weight of the rope and the weight of the monkey. What was the length of the rope? Miss Collins assures us that this is a perfectly genuine problem. Unfortunately, we believe her. Rescue, please, readers. Answers to Correspondents R. L. Matthews, Whare Flat: As you see, Mr. Etherington unravels the black and white discs tangle. ( We are pleased to report a satisfactory number of correct answers. Successful. readers should pat themselves on the back, We have insufficient space.) The beggar whose brother died was the brother’s sister, as you say, and a similar trick worked for the man who met the woman on the road and knéw the daughter’s name was Mary. Your first poser had crossed our bows before, but thank you for the reminder. Have already wasted too much paper on the second so have handed it over to our milkman, R.J.G.: We should have mentioned in the note in our last issue that the level crossing problem had come in previously, |