SUCCESS OF A SEPTUAGENARIAN

New Zealand Listener, Volume 3, Issue 56, 19 July 1940, Page 21

SUCCESS OF A SEPTUAGENARIAN

see The. Listener puzzles. In the course of his less strenuous duties the Puzzle Editor often calls on Men of the Moment and Men of the Hour and things like that and if it’s on a Wednesday, when the posters first go out on the streets, more than often you find. them with their secretaries busy with pencil and paper drawing little diagrams and sending the messenger out for a copy of a lower-form geometry book or logarithm tables. And they are not all young men. Proof that the ancient and hoary retain their metaphorical noses for a problem arrived, for instance in this week’s mail. From Plimmerton "Invicta" writes to say that he is 75 years of age but has completed (word underlined) the chessboard problem. "After many long trials," he explains, "extending over five days. . Many times I was within one of right, Thirty-seven and 38 would not fit, and once the first 63 (underlined) were right but 64 was, alas, next door! Invicta sends his answer, which differs from the one from L.G.L., Motueka, printed last week. We therefore reproduce it: L: really is extraordinary where you

The Matches Correspondence this week also includes a note from "Newcomer," who whiles away the time in the wilds of Arthur’s Pass by bettering the solution given for F. Lovell’s "Want to Play with Matches Ploblem" (June 14), Instead of a series of contiguous parallelograms, Newcomer suggests that the 12 remaining hurdles be fitted in the shape of a hexagon, giving 6 pens as made by 13 hurdles. Bricks As it is a very long time since we had one like this, we also print Newcomer’s Problem of the Brick: A brick weighs seven pounds and half a brick; what is the weight of a brick and a half? Shunters Hammering away at the shunting problem given by Tane in the issue of May 24, G. Tisbury, of Invercargill, claims that we were wrong in suggesting that the trucks might not be pushed by hand. He says that shunters often do it, and can easily push one or two trucks. We had suggested that this was hard work and that the engine should be made to do the job. To retain the difficulty of the problem (which involved exchanging the positions of two trucks on a loop, with an engine on the main line and the loop divided by a deadend which would hold only one truck) we have to insist that this shunter must be lazy, and used the engine only. G.T. also suggests that a dead-end Iolds

nothing. To clear up all this confusion, we give a diagram showing the whole works.

The dead-end (DE) holds only one truck, but from there, of course, a truck can be shunted into either half of the loop. The positions of trucks 1 and 2 have to be exchanged, using only the motive power of the engine on the main line. Bottles of Wine By way of a bribe for the above, G.T. sends this problem: A gentleman who kept some bottles of extra fine wine in a special place in his cellar, had a suspicion that the servants were stealing them. He devised a trap, and went to the cellar to arrange his 28 bottles like this: yas 2 be See 11111 11111 bE age & Se | This gave him nine along the top row, nine along the bottom, and nine adding up either side. At the first chance, the butler snooped into the cellar, noticed the regularity of the arrangement, and decided that he could remove four bottles and yet still leave the same rows totalling nine. He did so. The owner noticed nothing, and soon after the butler took four more, and again re-arranged the bottles to give the totals of nine, up and down, and across. Still the owner noticed nothing. In what way had the butler re-arranged the bottles? Answers Tommy and the Pie: It should quickly be noted that every multiple of 8 falls on Tin No. 2 in a backwards direction. Therefore 555 divided by 8 equals 69, plus 3 remainder. Three more counts after No. 2 brings Tommy to Tin No. 3. (Problem and answer from R.G., Waihi.)

Trees: 27,889 trees. Originally there were 27,667 trees, forming a square 166 x 166, with 111 over. With the addition of 222 trees, they were planted in a Square 167 by 167. A correct answer came from R.G., who notes that half of 333. is 166%, and that difference between 166 squared plus 167 squared is 333. There were 166

squared trees in the plantation. at first (27,556) and therefore there must be 167 squared in the finished plantation (27,889). The difference between any two consecutive squares is always odd (says R.G.). Halve this difference and the two whole numbers lying either side of the result will give the side of the squares before and after the operation respectively. Condensed Crossword: 7. eth E Ss T ae ow > rH Ww

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