In three-dimensional chess, how few rooks are needed to checkmate a lone king?

competition/games/chess/rooks.3d.mate New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

In three-dimensional chess, how few rooks are needed to checkmate a lone
king?

[ Editor: problem statement reconstructed from the postings.  The
original question (by Angel Omer, 1994) is not in the collected
material; a reply suggests that it proposed 1000 rooks. ]

Show solution

B. Despres (bdesp@wpi.edu) wrote:
> easily...
> 6 rooks can do it.  1000 is a wee bit of overkill.

[ Editor: another poster, not named in the collected material, replied: ]
> I can only see a solution with 9:

Nah, I see seven, but I would like to see the 6'er solution!

rxx
rxx
rxx
 xxx
 xkx
 xrr
  xxx
  xxx
  xrr

-- Mark Stieffenhofer <stiemark@astro.ocis.temple.edu>
   (reposted by Karl-Eric Pause <kpause4@mach1.wlu.ca>)

[ Editor: the diagram shows three successive 3x3 layers around the king
(k), with r for a rook and x for a square; it holds seven rooks.  The
six-rook solution was not given in the collected postings. ]