  In this paper we are concerned with knight's tours on high-dimensional
boards. Our main aim is to show that on the $d$-dimensional board $[n]^d$, with
$n$ even, there is always a knight's tour provided that $n$ is sufficiently
large. In fact, we give an exact classification of the grids $[n_1] \times ...
\times [n_d]$ in which there is a knight's tour. This answers questions of
DeMaio, DeMaio and Mathew, and Watkins.
