17 blue connecting segments
Source: Bundeswettbewerb Mathematik 1991, round two, problem 2
June 19, 2004
inductiongraph theorycombinatorics solvedcombinatorics
Problem Statement
In the space there are 8 points that no four of them are in the plane. 17 of the connecting segments are coloured blue and the other segments are to be coloured red. Prove that this colouring will create at least four triangles. Prove also that four cannot be subsituted by five.
Remark: Blue triangles are those triangles whose three edges are coloured blue.