Enigma 216: Point to point
22 August 2014
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From New Scientist #1362, 16th June 1983 [link]
As a challenging geometry puzzle, I asked my son to mark a prescribed number of points on a piece of paper, no three of them being in a straight line, and then to join each of the points to each of the others by straight lines. I knew by my choice of the number of points that he would not be able to do this without at least two of these lines crossing.
But I asked him to do it with some of his lines drawn in red, and the rest drawn in blue, and in such a way that it would be impossible to find a red triangle or a blue triangle in the whole configuration. This he managed.
How many points had I asked him to draw?
Note: I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.