Given is an infinite 3-dim chess board and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite number of moves?


(In 3-dimensional chess rooks move in straight lines, entering each cube through a face and departing through the opposite face. Kings can move to any cube which shares a face, edge, or corner with the cube that the king starts in.
See [Wikipedia](http://en.wikipedia.org/wiki/Three-dimensional_chess)).


**Update:** Comments (below the line) give interesting information on this problem including a connection to Conway's angel problem with 2-angel (Zare) and interesting comments towards positive answer and connection with "kinggo" (Elkies). Also a link to an identical SE question is provided [MSE Question 155777](https://math.stackexchange.com/questions/155777/guaranteed-checkmate-with-rooks-in-high-dimensional-chess) (Snyder).



Rooks in three dimensions
As far as I know, it is still open whether or not there is any finite number of rooks which can force checkmate. However, this is possible. I answered the question over at [math.stackexchange](https://math.stackexchange.com/a/156693/1321) describing a strategy which forces checkmate with 96 rooks. This is certainly not optimal. The strategy I describe is very wasteful, keeping some rooks in place even when they are not actually needed, so it can be improved at the expense of becoming more difficult to describe.


