Let $G=(V,A)$ be a graph in which every pair of vertices $k_i , k_j \in V (i \neq j)$ is connected by some arrow $(i,j) \in A$. Let's call this graph a tournament. Furthermore, let this tournament be non-transitive. This means that if there are arrows $(i,j)$ and $(j,k)$, this implies that there is also an arrow $(i,k)$.
Question: How does one show that a non-transitive tournament always has at least three different Hamilton paths?
I can see this is true for some examples, but I can't figure out how to prove this statement.