FINALE FOR THE PAGE

New Zealand Listener, Volume 4, Issue 82, 17 January 1941, Page 47

FINALE FOR THE PAGE

HIS is the finale for The Page -not a very grand one, but necessary. One or two letters have arrived since*our demise was announced on December 27. E.A.C. writes sympathetically and sheds a tear with and for us. He says: "I am deeply sorry that one of my favourite sources of amusement and relaxation has gone... . My family also ‘will miss my getting into tempers and refusing to go out till I have finished that problem." The PP does not feel at all immodest about transcribing one or two of these small tributes. They are not, after all, to him, but to The Page, which was nothing if not the work of the correspondents, A.S., of Taumaranui, is in at the death. This new correspondent wrote on December 23 to say: "I often have a glance at The Page and think the problems very good ... and at times take a@ power of unravelling. An hour or two passes before you realise it. You provide pleasure and entertainment for a great many, I am sure." He hopes he will be carrying on the good work. ... Rob, of Ahipara, like E.A.C., and so many dozens of others, is an old friend. Rob says: "The Page has passed many an hour of semi-forgetfulness of pain for me. I have been in bed since April .- » . on my table are sheets of problems. . . " However, Rob seems to make a good deal of his own fun. A small friend poses him such problems as: "Which way would the smoke go from an electric train if the train was going north at 60 m.p.h.?" Rob counters such queries with something like this: "What animal on a farm has a counter, a star a muzzle, a cannon, and a coronet?" A win on points went to the small boy, who announced after one week’s grace that the electric train was being pulled by a steam engine. (He had seen this happen somewhere). Rob announced that his animal was a horse. So it goes on. Rob writes about the fun he has with himself and his friends, and The Page, and the PP has indeed been pleased to find himself in such pleasant company. Rob’s letter cannot be fully reproduced, which is a pity, but we hope and expect that it gave him sufficient pleasure in the writing. Dear Rob, we’d really like to print it all, and thank you. A glance back through the file brings the PP to one of E.H.C.’s letters. Phew! Hope 1941 finds this correspondent in better spirit. In the general atmosphere of good cheer we find it quite impossible to match his argumentative mood. Good luck to him, and good-bye. "Tane" does not seem to have had the space he deserves for his exposition of The Monkey and the Rope problem (November 22 and December 6). "Tane" discusses the points raised by H.G.L. on, December 6. He says the first was correct, and the second, but that the third was wrong: "While the monkey attains and maintains a constant speed towards the pulley, the weight does the same towards the pulley. As the monkey slows and stops, the weight slows and stops." "Tane" continues: I have assumed that the inertia effect in the rope and pulley, and friction in the air, rope, and pulley bearing, may be neglected, though we must allow friction between the monkey’s hands and the rope. The point about the rope lerigthening behind the

monkey and increasing in weight may be eleminated by joining the ends of the rope. Now: the monkey at rest pulls on the rope with a force equal to his weight. In accelerating towards the pulley he increases his pull on the rope until he has attained a constant velocity. This increased pull on the rope is transmitted over the pulley to the weight, and acts on it, giving it exactly the same acceleration and velocity as the monkey. When the monkey attains his constant speed his pull on the rope returns to an amount equal to his weight. The weight, on the other side of the pulley, is then acted on by two opposing forces, gravity and the pull of the monkey. These, being equal, cancel out, and the weight, being in motion towards the pulley, continues in that motion. (Newton’s laws). When the monkey slows down and stops, the weight slows down and stops at the same time. It will be noted that while the monkey is climbing the rope passes through his hands twice as fast as he climbs." "Simple Simon," of Hawera, wanted to know early in December, concerning the problem about the murderer who was released and found the person he had murdered still alive, how the police had secured a conviction without a corpse to display. A good point, surely? "Sylvia," about the same matter, believed that the man released from prison, having bought the other man’s life with a prison sentence of 20 years, was entitled to despatch it. E.H.C. wrote about our "notorious" ladders sproblem in which heights of ladders were given and in which it was required to find the height of their intersection when placed from opposite sides across an alley. He says this problem, or one similar, has appeared in Esquire. (Rob, please note, in answer to his inquiry) and that the lengths, and not the heights, of the ladders, were the stated factors. Which made all the difference. Puzzlers who have kept The Page filed might like to turn back and see how this suggestion affects the problem. A later letter from E.A.C. arrived at this moment (January 6), argues about T.M.C.’s geometrical proof (January 3). However, as he points out only that the fallacy lies in the drawing, it can probably be left at that. E.A.C. argues that, if the triangle is isosceles, AO and TO are the same straight line, but that is arguing from the right end of the

problem, whereas the most interesting result is achieved by arguing from the wrong end. All clear? Here are some problems discovered on the file. The answers are given too, but puzzlers are trusted not to look until they’ve tried: