I'd like to compute the number of edges necessary to build all Hamiltonian paths in a complete digraph.
My thoughts so far:
Let $N$ be the number of nodes.
- number of Hamiltonian paths: $N!$
- number of edges per path: $N-1$
- total number of edges necessary to build all paths: $N!*(N-1)$ (assuming an edge gets consumed when building a path)
I have a given solution: $N!*N$
Can someone explain where the extra factor of N comes in?