So, say you have 16 points (0-indexed):
You want to walk across the vertices, skipping over a specific number of them, landing on the end vertex. You can always 1-connect them:
But 2-connecting 3-connecting, 4-connecting, $X$-connecting is only possible if ${N-1}\mod{X}=0$, $N$ is the number of vertices.
Why isn't it $N \mod x=0$?