Enigma 162: Quoit utilities
18 January 2014
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From New Scientist #1307, 27th May 1982 [link]
The diagram is a map of a quoit (that is, of what topologists call a torus or a doughnut). The map can be made into a quoit by rolling it up so that the edges AB and DC coincide, and then bending it around — the map is printed on stretchy material — so that the rolled up AXD coincides with BYC. Thus the two E‘s coalesce, and so do the two 1’s.
As you know, you can’t connect three utilities, E, W and G, to each of three houses, 1, 2 and 3, on the surface of a sphere, without any pipe crossing another. But, as the map shows, you can do so on the surface of a quoit. In fact, you can do even better. You can connect E, W, G and V to each of the four houses. What I ask you for is a map showing how. The map must be a rectangle of squared material, cut at any angle so long as the edges match when the map is made into a quoit. E, W, G, V, 1, 2, 3 and 4 are to be at intersections of the material, and all the pipes are to run along the grid lines without touching or crossing.
Finally, I want a map with the smallest possible area. You will find you can manage with a lot less than 60, which is the area of the map in the diagram.