  The present paper aims to extend the knight's tour problem for
$k$-dimensional grids of the form $\{0,1\}^k$ to 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 $k \geq 15$. Our result considers the three
above-mentioned leapers and replicates for each of them the recent discovery of
Euclidean knight's tours for the same set of $2 \times 2 \times \cdots \times
2$ grids, opening a new research path on the topic by studying different fairy
chess leapers that perform jumps of fixed Euclidean length on given regular
grids, visiting all their vertices exactly once before coming back to the
starting one.
