Knight's tour is very well known problem, but what about rook's tour? On $n\times1$ chessboard there are obviously $n!$ open and $(n-1)!$ closed tours.
Is there a way to easily compute number of open and closed rook's tours on $n\times m$ (or just for some small $m$) chessboard? Question doesn't look trivial, so I don't know what can be added to make it more informative. I will appreciate any references.