Answers + The Monkey and the Rope + More Word Sums + He Caught the Tram

New Zealand Listener, Volume 2, Issue 27, 29 December 1939, Page 55

Answers + The Monkey and the Rope + More Word Sums + He Caught the Tram

readers the opportunity to look up the answers to our puzzles. But this seasonal generosity could not last. With this, the New Year issue, we suggest that a good resolution is timely. Since our school days we've always thought that "Answers on Page-" was a dangerous way of escape, so we're back on the basis of keeping readers in the dark until our Puzzle Puddler is ready to enlighten them, Usually, of course, the answers appear in the issue following publication of the problem. But with especially difficult ones we like to give readers more time to work them out (if they can!) Now for some _ retrospection. On December 15 we posed the numerical code problem about SALOME, the Lift Attendant word-trickery, the problem of the bottle and the cork, and Miss Collins's Monkey Puzzle. Unluckily, as explained on December 22 (Page 38) the first version of the Monkey Puzzle suffered from a misprint. We hope readers were able to make more sense of the reprinted problem last week. With these small points cleared up we can discuss answers: The lift attendant would know his own name and age. The cork cost one farthing. The length of the rope was 50 feet. SALOME represented 142857, The Monkey Puzzle To elaborate: Miss Collins, contrite, sent in answers to her puzzles-too late to save us from working them out, but in time to supply some interesting comment on methods. To work out the Monkey Puzzle she started at the end of the sentence, "The monkey’s mother is twice as old... three times as old as the monkey," and worked step by step backwards, giving X years as the age of the monkey, at that stage, and 3X as the age of the "mother. From this process, she secured the information that 5X plus 8X equalled the combined ages of the monkey and the mother. This was given in the problem as 4 years, so she had the algebraic equation: 5X +3X=4 So that: 8X = 4 So that: X= If X (the age of the monkey when the mother was three times as old, etc.) I: our Christmas issue, we gave

equals 4, then the age of the mother is 24 years and the age of the monkey 44 years. That gives the monkey’s weight as 24 pounds. And that, with W as the symbol for the weight of the rope, gives the following sequence of equations, working from the second to last sentence: W + 23 144 (W- 24) 50 W + 5/2 = 3/2 (W — 5/2) so (multiplying by 2) | 2W+5=-3 (W-- 5/2) = 3W — 15/2) so (multiplying by 2) | 4W + 10 = 6W — 15 so (transposing) | 2W = 95 ear. Se == 124 (pounds) = 200 ounces. As every 40 ounces equals one foot, the rope is 50 feet long. Q.E.D. The problem, of course, could be solved without recourse to algebra. He Got in First Miss Collins also supplies the answer to the SALOME word-sum, but W. R. Hamer, Foxton, was in first, so we

acknowledge his correct answer and the industry which prompted him to send two variations that put us, as he said we had put him, "in a whirl." To solve SALOME x L to LOMESA x L to MESALO, L was found to be 2, and the rest, we hope, was easy: SALOME 142857 © L 2 LOMESA 235714 L 2 MESALO 571428 Coloured Shirts The mathematical precision used by Miss Collins to solve the Monkey Puzzle was equalled by the neat conception of a method to work out the problem of the coloured shirts, which we answered out of our small ability on December 22. Obviously, a process of elimination had to be used, so Miss Collins drew three diagrams like crossword squares or the tables used to score in Yankee tournaments, where everyone plays everyone else. She had one for shirts and commanders (shirts down and commanders across), one for commanders and seconds, and one for shirts and seconds. As she went through the clues she indicated her eliminations with a cross in each appropriate square, thus saving a mental process which caused us quite a few minutes intense concentration. This simplified a complicated process as much as it could be simplified; but if any one wants to go the other way,

and make things more complicated, let him (or her) take the problem as originally printed and play with the positions of the apostrophes. We confess that this idea came from a careless interpretation of that elementary grammatical rule when we first’ tried to work out the shirts problem. Word-Sum Now for next week’s homework: Here is Mr. Hamer’s word-sum: SALOME multiply L LOMESA plus SALOME ALOMES plus SALOME MESALO plus SALOME ESALOM plus SALOME * OMESAL And Still ‘Another And still ‘another variation a little more obscure: SALOME (14) -+ SALOME LOMESA (2) + SALOME ALOMES (3) + SALOME MESALO (4) + SALOME ESALOM (5) + SALOME OMESAL (6) As if this were not enough, Mr. Hamer adds: ‘And now here’s one to ‘quicken your baldeas." #5 Here it is: Mr. Busy, at the same time each day, turned a corner 90 yards from the tram stop. The tram was at the stop further down, the stops being 240 yards apart. Mr. Busy could do- 400 yards to the tram’s 240, so he always caught his fram. On one particular morning, however, he had rheumatism, and, as it was imperative that he catch this last tram to town, he hurried as fast as he could, but found that he could only do 80 yards to the tram’s 240 yards. He turned the corner at.the same time as usual and the tram was never late. The driver was one of those people who would not wait for anyone, even if he were driving the last tram. The tram did not reduce speed, nor did Mr. Busy get a lift. Yet he caught the tram with time to spare. How? And s0, ase next. week, How? Busy Mr. Busy