Could you place seven dots on a plane, such that for any three points out of the seven, if you draw a triangle between them, at least one of the edges will be of size 1"?
Notice that for six points, this is trivial. Draw two unilateral triangles (1" each edge), T1 = {a1, b1, c1} and T2 = {a2, b2, c2}, this gives you six points. If you draw three points from the union, then by pigeon hole principle, two of the points will belong to the same triangle. They will have a 1" edge between them.
Find such seven points or prove impossible.