There exists a triangle with all edges of the same colour.

Question

Let there be a pyramid with a nonagonal base. The lateral edges and the diagonals of the base are drawed with black or red.

I have to show that there exists a triangle with all edges of the same colour.

I have no idea how can I start.

Answer 1

If $V$ is a peak of pyramid then $V$ is connected with at least 5 different base points with the same color say black. If two of these 5 are connected with black diagonal then we are done.

So suppose each pair of these 5 points which is connected is connected with red diagonal. Now it is not difficult to see that some 3 of them are not such that are pair vise not neighbour. So these 3 make a red triangle.