A problem in my book is:
Let the edges of $K_7$ be colored with the colors red and blue. Show that there are at least four subgraphs $K_3$ with all three edges the same color (monochromatic triangles). Also show that equality can occur.
By the theorem on friends and strangers it is clear that 1 monochromatic triangle exists. Deleting a vertex of that triangle and applying the theorem again yields another. Why are two more guaranteed?
As an aside, a result in my book states that the number of monochromatic triangles in a 2-colored $K_n$ is at least $\binom{n}{3}-\lfloor \frac{n}{2}\lfloor (\frac{n-1}{2})^2 \rfloor \rfloor $. I want to demonstrate my solution without applying this result though as it appears later on in the book.
Thank you for your time.