# Suppose the edges of a complete graph of $10$ vertices are coloured each either blue or red. Show that there is a blue triangle or a red tetrahedron

Could I get any help with this one, I'm lost.

We know that the Ramsey number $$R(3, 3)$$ equals $$6$$. Suppose the edges of a complete graph of $$10$$ vertices are coloured each either blue or red. Show that there is a blue triangle or a red tetrahedron (i.e. a complete graph on 4 vertices all of whose edges are coloured red). [Try to use the pigeonhole principle with unequal parts.]