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.]