3D chess
B. Despres
: on an infinite 3 dimensional chess board, can 1000 rooks mate a lone
: king? a rook can change one of it's coordinates to anything, and a king
: changes each of it's coordinates by no more than 1.
easily...
6 rooks can do it. 1000 is a wee bit of overkill.
- pla
Saied Bozorgui-Nesbat
==>Angel Omer (s319...@techst02.technion.ac.il) wrote:
==>
==>: on an infinite 3 dimensional chess board, can 1000 rooks mate a lone
==>: king? a rook can change one of it's coordinates to anything, and a king
==>: changes each of it's coordinates by no more than 1.
==>
==>easily...
==>6 rooks can do it. 1000 is a wee bit of overkill.
==>
==>
==>
==> - pla
==>
==>
6 for a Draw, 7 for a MATE!
Cheers!
Saied
Angel Omer
on an infinite 3 dimensional chess board, can 1000 rooks mate a lone
Mark Stieffenhofer
: Angel Omer (s319...@techst02.technion.ac.il) wrote:
:
I can only see a soultion with 9:
rxx
rxx
rxx
rxx
rxk
rxx
rxx
rxx
rxx
This way any of the possible 26 moves are covered.
karl-eric pause 9208 U
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From: stie...@astro.ocis.temple.edu (Mark Stieffenhofer)
Newsgroups: rec.puzzles
Subject: Re: 3D chess
Date: 5 Aug 1994 04:45:16 GMT
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>B. Despres (bd...@wpi.edu) wrote:
>: Angel Omer (s319...@techst02.technion.ac.il) wrote:
>:
>: easily...
>: 6 rooks can do it. 1000 is a wee bit of overkill.
>:
>I can only see a soultion 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
Saied Bozorgui-Nesbat
==>
==>From info!torn!howland.reston.ans.net!newsserver.jvnc.net!netnews.upenn.edu!cronkite.ocis.temple.edu!astro.ocis.temple.edu!stiemark Fri Aug 5 12:17:03 1994
==>Path: info!torn!howland.reston.ans.net!newsserver.jvnc.net!netnews.upenn.edu!cronkite.ocis.temple.edu!astro.ocis.temple.edu!stiemark
==>From: stie...@astro.ocis.temple.edu (Mark Stieffenhofer)
==>Newsgroups: rec.puzzles
==>Subject: Re: 3D chess
==>Date: 5 Aug 1994 04:45:16 GMT
==>Organization: Temple University, Academic Computer Services
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==>==>>: easily...
==>>: 6 rooks can do it. 1000 is a wee bit of overkill.
==>>:
==>
==>>I can only see a soultion 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
==>
==>
hmmm 7 it is; with a friendly king who volunteers to move into the kitchen of course!
Saied Bozorgui-Nesbat
==>Saied Bozorgui-Nesbat <sai...@sinbad.eng.sun.com> wrote:
==>>==>: on an infinite 3 dimensional chess board, can 1000 rooks mate a lone
==>>==>: king? a rook can change one of it's coordinates to anything, and a king
==>>==>: changes each of it's coordinates by no more than 1.
==>>
==>>6 for a Draw, 7 for a MATE!
==>I can see how to get a mating position with 7 rooks, but I can't figure
==>out the mating procedure. Can you explain?
==>
==>Dave Ring
==>Cd...@phys.tamu.edu
hmm! A lot happens when one tries to explain.
Now I believe it is IMPOSSIBLE to put an albeit cooperative king in a mate position with anything less than 9 rooks!! But minimum of 9 in necessary and not sufficient.
Alas, the more I think about this the more I am convinced that the the number necessary to guarantee a mate has no bound! Can't be done methinks.
Send in the queens!!
Cheers!
Saied
David Wayne Ring
>==>: on an infinite 3 dimensional chess board, can 1000 rooks mate a lone
>==>: king? a rook can change one of it's coordinates to anything, and a king
>==>: changes each of it's coordinates by no more than 1.
>
>6 for a Draw, 7 for a MATE!
I can see how to get a mating position with 7 rooks, but I can't figure
out the mating procedure. Can you explain?
Dave Ring
Cd...@phys.tamu.edu
Mike Paterson
That's a nice problem. A variation of this (which is closely related to
a problem of Conway's, "Angel(!) and Square-Eater", which I believe is still
open) is the following.
Replace the king by a "superking" which can in one move change each of it's
coordinates by no more than 100.
Is there any finite number of rooks which can mate it?
Mike Paterson
--
Scott Bales
position for only 6 rooks (plus king):
RRxx
xxxx
xxxx
RRxx
xkxK
xxxx
RRxx
xxxx
xxxx
However, as previously noted, I believe the original poster wanted an algorithm by
which some number of rooks could force an *uncooperative* king into a position in
which he could be checkmated. I've convinced *myself* that this is not possible,
due to the fact that the king can change its position in all three dimensions, while
the rooks are limited to motion in only one. However, I've been unable to come up
with a compelling proof. Can anyone help?
While we're at it, let's add a couple more puzzles:
1) Assuming we define a queen as a piece that can go in a straight line in any
one or two dimensions (in other words, can move like a normal 2-d queen in any
given edgewise plane), is there a minimum number of such pieces that could force
checkmate on a lone king on an infinite 3d chessboard? What is the general
algorithm?
2) Now assume we define a "hyper-queen" that can move in a straight line in
1-, 2-, or 3-dimensions. Same questions as above.
- Scott