By Stephen Barr

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**Additional info for Second Miscellany of Puzzles : Mathematical and Otherwise**

**Sample text**

Didn't think of it. Left them both in the shed. Anyway, it doesn't matter-I can work it out with elementary geometry. Just the thing for measuring the elements. " What was the thickness, and how did he do it? ) 53 34 DRAFTING PUZZLE A draftsman has no instruments but a compass, and a sheet of paper which he does not fold, and which can be bought at any stationer's. How does he establish and mark the six vertices of a hexagon with only one placing of the point of the compass? 54 35 THE PSYCHEDELIC CUBE Optical illusion is not new in the arts; any realis- tic picture in perspective is an optical illusion.

FIGURE 1 FIGURE 2 FIGURE 3 68 49 THE NINE DIGITS Excluding zero, the nine digits are written down in any arbitrary order (first line, Fig. 1). Under these we write the ordinal numbers that give the positions of the digits in the first line. Thus we start with 7, because in the first line 1 is the seventh number; then we write the number that gives the position of 2, in this case 6, and so on. We shall call this operation X. If we now apply the operation to the second line (Fig. 1), it gives the first line again.

54 35 THE PSYCHEDELIC CUBE Optical illusion is not new in the arts; any realis- tic picture in perspective is an optical illusion. Parenthetically, such pictures are abstractions-of a three-dimensional reality-whereas so-called abstractions, not being of anything, would be more correctly termed concretes, or Aldens, since they speak for themselves. A perspective representation is the projection by lines converging to a point of a three-dimensional object onto a plane. It differs from orthogonal projection in that the latter uses parallel lines.

### Second Miscellany of Puzzles : Mathematical and Otherwise by Stephen Barr

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