Euclidean tours in fairy chess

The present paper aims to generalize the Knight's tour problem for $k$-dimensional grids of the form $\{0,1\}^k$ by considering other fairy chess leapers. Accordingly, we constructively show the existence of closed tours in $2 \times 2 \times \cdots \times 2$ ($k$ times) chessboards concerning the Wazir, the Threeleaper, and the Zebra, for all $k \geq 15$. This extends the recent discovery of Euclidean Knight's tours on these grids to the above-mentioned leapers, opening a new research direction on fairy chess leapers performing fixed-length jumps on regular grids.