Is it possible to arrange seven points in a plane so that any subset of three points will contain at least one pair that is exactly 1cm apart?
Reveal Solution
Yes – the diagram below shows a possible arrangement.
{B, C, D, E, F, G} has a pair from either {B, C, D} or {E, F, G} which will be 1cm apart. If A is included then either B, C, E or F is there (which are all 1cm from A) or both D and G are there which are 1cm from each other.
