So I came across a pigeonhole principle question and was unable to complete this question. I was just wondering how to commence this question/what sort of reasoning I could use to "explain". Proof by contradiction is always an open method but I'm unsure how to apply it into this question here.
A regular octahedron has $6$ vertices. Each vertex is connected to each other vertex by a rod that is coloured yellow or blue.
$1.$ Each set of three vertices, together with the rods joining them, forms a triangle. Explain why there are $20$ such triangles.
$2.$ Explain why there will be at least one triangle whose rods all have the same colour.