Download e-book for kindle: Scholarship Mathematics, Volume 2: Geometry by Arthur Tisso Starr

By Arthur Tisso Starr

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Sample text

The object is simply to fit the pieces into the tray. What makes it tricky is that the picture frame opening on the top is only 4 × 4. There is only one solution. (This is the simple version. ) This next puzzle, Looking Glass, does employ a slot in the side of the square 5 × 5 tray through which the six polyominoes are inserted (Figure 57). The round hole in the plexiglass cover is simply to facilitate sliding the pieces about with the eraser-end of a pencil. The one solution is not straightforward, especially for some popular puzzle-solving computer programs, as it involves rotation.

In trying to solve this puzzle, one might start by assuming that Dudeney probably placed the square piece symmetrically in the center for aesthetic reasons. ) With the 2 × 2 checkered square thus centered, by placing the cross piece in each of its four possible locations, one discovers the impossibility of any such solution. This puzzle is known to have four solu- Chapter 2. Two-Dimensional Combinatorial Puzzles 27 tions, but all with the square piece off-center. Did Dudeney introduce this slight aesthetic anomaly just to confuse us?

Try to fill the corners first, the ends next, and work toward the center. For an even more methodical (but less entertaining) approach, consider how a complete analysis of this puzzle might be made. Number the spaces on the 6 × 10 tray 1 to 60 as shown in Figure 34. Always try to fill the lowest numbered unfilled space with the lowest numbered remaining piece. So, start by placing piece no. 1 on space no. 1. Since this piece has no symmetry, it can be oriented four different ways by rotation plus four more when flipped over, six of which will cover space no.

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Scholarship Mathematics, Volume 2: Geometry by Arthur Tisso Starr


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