19 September 2011

Mind Games 7: Answers

Answers 22-23

22. Strictly speaking, this puzzle is impossible to do in two dimensions – in other words, on a flat piece of paper or a screen. Except for this cunning solution: let one of the lines pass THROUGH a house to get to the other houses! Look at the yellow line in this diagram:

And there’s another, advanced solution, using a mathematical shape called a torus (really just a fancy word for “doughnut”): if you drew the houses, utilities and all the lines connecting them on the surface of the torus, with one line going through the doughnut-hole, it would be possible to do it all on one “plane” without crossing or touching. (You could emulate this effect by punching a hole in your paper diagram and drawing on both sides.)


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