Show that if the edges of $K_n$ are colored with $n$ different colors, then there must be a triangle where all three edges have distinct colors.
So, I want to use induction on $n$ where $n$ is the number of vertices in the graph then the base case would be $n=3$ ($K_3$ graph) because you must have a triangle with three distinct edge colors. Then, I know if I draw it with $n=4$ and so on so forth it is true, but I'm having trouble putting it more eloquently.
Hint: Remove one vertex from $K_n$. If the remaining graph is coloured with more than $n-2$ colours you can use induction, otherwise there are at least two colours that are not in remaining graph.