MAINLY FOR MATHEMATICIANS

New Zealand Listener, Volume 2, Issue 39, 21 March 1940, Page 16

MAINLY FOR MATHEMATICIANS

EXT week, puzzlers, will be a special French issue, so we're starting early. This week we are going to discuss figures. And, to show that we mean business, we'll start right away. During the last month a fairly select group of readers has been busy with the higher flights of

mathematics. We’ve been saving them, and here’s the horrible result: Obviously, you will say, this table requires some explanation. It does not take all that space for nothing. Well, it comes from H. D. Mullon, of New Plymouth, who worked it out according to a rule. If. you care to check it, you will find that each row, perpendicularly and horizontally, adds to 1105, that the diagonal addition is also 1105, and that the number of rows multiplied by the centre figure (85) makes 1105. Obviously, you will also say that this is remarkable. It is remarkable. But it is not unique. More Figure Squares From S.G.E. (Glenavy), comes a whole collection of similar figure-squares. He gives six, each larger than the first. In the first, he has five figure-groups to each side of the square, built up to total 65. In four others he has six, all adding to 111. In the last he has seven groups per side, all adding to 175, ‘And that is not all, You are not to be let=-down lightly this time, whatever leniency we have shown in the past. From W. H. Presswood (Whangarei), comes a letter covering the same sort of trickery. Mr. Presswood uses one square built ‘on five groups per side to total 65 (to illustrate his exposition of the rule) and another example with nine groups per side to total 369.

Now, read carefully, for there’s some explaining to be done. Study Mr. Mullon’s table. Observe that the centre row is headed by 1. This is where he started to make his table. His next move, to place the figure 2, would have ordinarily been to the diagonally adjacent square above the 1. But there is no square in this position, so the 2 goes into the bottom square of the vertical row of squares to the right of 1. From 2, he has gone diagonally

above and to the right as per the recipe until he has come to 7. Beyond 7 there is no square, so he puts his 8 in the other end of the row of figures immediately above the row terminated by 7. Then from 8, he runs consecutively up to 13, and here he finds that his next square, diagonally above and to the right of 13, is already occupied, by 1. So he establishes a rule that, when the next square is occupied, the next number shall go vertically below the last figure. So 14 goes below 13, and from there he runs easily up to 16. Here again, he finds no square ahead of him, so drops to the bottom of the adjoining row on the right and starts working diagonally once again from 17 to 21. Then up one and back to the other end for 22, and so on. How It Is Done So he establishes the rules: Start with 1 in the top centre. When there is no square for the next move, go one to the right and down to the bottom, if working at the top of the table, or one up and along to the left if working at the side. If the next square is occupied, use the one directly below. In the top right hand corner, of course, the rule does not apply, so he just drops 92 one square vertically below 91. Readers whose appetites have now been whetted should refer back to J. A. Reid’s statement on figure squares in our issue of February 2. Mr. Reid had still another method. A variation comes with Mr. Presswood’s examples. He gives the following table for his illustration,

This gives 65 in all directions. Mr. Presswood’s instructions are: Always start with 1 in the centre of the far vertical row and work diagonally towards the top right hand corner, as, for example, from 11 to 15. When you come to the edge, carry on at the beginning of the next line (see 1 to 2). When the next square above is already occupied go to the square to the left of the last figure in the same row (see 5 to 6). And that, of course, is simply Mr. Mullon’s method turned on its side, PROBLEMS The Rude Rowers Now for those humble folk who like plain puzzles. They will want something nice and easy. S.G.E. supplies this one: In celebration of victory in their annual rowing contest with the neighbouring school, students were believed to have been responsible for tarring and feathering a statue in a public park. Suspicion pointed to the rowing eight and their cox. The principal called on them and asked each one to confess. This is what they said: A-E did it. B-No, it was not E C-I did it. D-It was either C or H. E-B is not telling the truth. F-It was C. G-lIt was not C. H-lIt was neither C nor me. I-H is right, and it wasn’t E either. On the assumption that three statements are true, who despoiled the statue? lrish Arithmetic Arrange 5 numbers, none of which is greater than 10, so that when read from left to right, the one on the right will always be nearer to 10 than the preceding one, and the first number will be nearer to 10 than the fifth, -- C.N.G,, (Gisborne). Double Acrostic For those readers who are not familiar with a type of puzzle which has not appeared previously on this page, and who are now prepared to stoop to solving this one, we might say that a double acrostic is a poem in which the initial and final letters of each line make words. This one: Means we've got On the spot. 1. The poet thus designates tears When he in the spirit appears. 2. Here we present (or maybe personate) The language (maybe) of some x future date.

3. This may be seen On cook and on dean. 4. Close application brings to. mind A carriage of a foreign kind. 5. A force Of horse. ANSWERS | _ Refer to The Listener of March 8. The Queening of Alice: If we place the ruler to pass through the point A (top right of Q. Kt. 5), it cuts off one-fifth; through B (top right of Q. 5) gives another fifth; and so on through C and D.

Tolls: Two half-pennies. Age: Forty-four. The only year between 1900 and 1940 divisible by 30 is 1920. Station: It was a mail train. Oranges: At a third gate he must have only one left, so start at the beginning with X as the number of oranges and construct a series of equations until you have become tired of algebra, then think swiftly for one second and say "six" in a confident voice. On second thoughts, which are always best, say "seven" and you'll agree with us. Egg: The problem was given wrongly. The fifth sale was the second last sale. Family: One man’s daughter married the other man. He married the othér man’s daughter. Jumps: An infinite number of jumps until the poor frog falls off, according to our hare and greyhound experts; but, the frog, we must presume, jumps the same distance each time he jumps. Unless he can jump one-third of the ten-foot log the proposition does not hold, so you just have to work it out on the assumption that he. jumps 3ft. 4ins. Changeling: The window is diamond shaped.

93 107 121 135 149 163 22 36 64 78 79 108 122 136 150 164 9 23 37 51 65 66 80 123 138 153 137 152 167 151 166 12 165 11 26 ene eee | 24 #39 41 38 40 55 52 54 69 53 68 83 67 82 97 81 96 111 95 110 125 94 109 124 139 168 13 14 28 42 56 70 84 98 112 126 140 154 15 29 43 57 71 99 113 127 141 155 169 16 30 44 58 72 86 100 114 128 142 156 157 31 45 59 73 87 101 115 129 143 144 158 17 46 60 74 88 102 116 130 131 145 159 18 32 61 75 89 103 117 118 132 146 160 19 aa 47 76 90 104 105 119 133 147 161 20 34 48 62 91 92 106 120 134 148 162 21 35 49 63 77

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