Kevin Pacey wrote on Sun, Feb 21, 2016 06:07 AM UTC:
I've been playing around with the idea of inventing a viable 4D version of Alice Chess, if it's possible, and I thought I'd put a diagram here to study at my leisure. With Directed Alice Chess III by Joe Joyce (an Alice Chess variant played using just 3 boards), for example, a way to make a 4D Alice Chess variant may have already been invented in disguise. That's since a bishop may be able to make a single square diagonal step move (forward or backward) when going onto each of 3 different 2D boards in single steps, as done on 3 consecutive turns, with the bishop possibly finishing on its starting board, but also possibly just one diagonal step from its original square on that starting board. This is not possible in a typical 3D chess variant (e.g. 5x5x5 Raumschach) with, say, a bishop that moves in standard 3D chess fashion, as the bishop could not even return to its starting board if visiting three of the 2D boards in single steps in 3 consecutive turns. However, it could be possible in a 4D variant (i.e. having 4 or more boards, normally, although at least one of the corner 2D boards might be voluntarily excluded), with a 'standard' 4D bishop still changing just 2 (of now 4) co-ordinates. It might also seem to be possible if using 3 somehow otherwise interconnected 2D boards than in typical 3D chess (as could be the case for Directed Alice Chess III), except that then I do not see how a typical bishop (changing 2 co-ordinates as it moves) could possibly finish on its starting 2D board being just one diagonal step away from the square it started on, after visiting 3 different boards in 3 consecutive moves (in the single step fashion I described above) without the interconnection being in effect 4 dimensional. Perhaps a math wizard might try to explain it to a layman like me, if my conclusion is wrong. Meantime, here's a link to Directed Alice Chess III, followed by my test diagram for a possible 4D Alice Chess variant idea:
http://www.chessvariants.com/index/msdisplay.php?itemid=MLdirectedalicei
[edit: my original idea to use four 2D boards for a 4D Alice Chess variant idea was to have it like Alice Chess as much as possible, but to allow up to 3 pieces of any colour to occupy any of a set of 4 corresponding squares (e.g. one set would be those with file & rank = a1). That's also with just the two kings additionally being allowed to take an enemy piece occupying any of the corresponding squares that they may move to on the way in finishing their move (thus a double capture move would be possible for a K), but then the only forcible 'basic' mate would seem to be K & Q vs. lone K, which is not totally satisfying for me.]
I've been playing around with the idea of inventing a viable 4D version of Alice Chess, if it's possible, and I thought I'd put a diagram here to study at my leisure. With Directed Alice Chess III by Joe Joyce (an Alice Chess variant played using just 3 boards), for example, a way to make a 4D Alice Chess variant may have already been invented in disguise. That's since a bishop may be able to make a single square diagonal step move (forward or backward) when going onto each of 3 different 2D boards in single steps, as done on 3 consecutive turns, with the bishop possibly finishing on its starting board, but also possibly just one diagonal step from its original square on that starting board. This is not possible in a typical 3D chess variant (e.g. 5x5x5 Raumschach) with, say, a bishop that moves in standard 3D chess fashion, as the bishop could not even return to its starting board if visiting three of the 2D boards in single steps in 3 consecutive turns. However, it could be possible in a 4D variant (i.e. having 4 or more boards, normally, although at least one of the corner 2D boards might be voluntarily excluded), with a 'standard' 4D bishop still changing just 2 (of now 4) co-ordinates. It might also seem to be possible if using 3 somehow otherwise interconnected 2D boards than in typical 3D chess (as could be the case for Directed Alice Chess III), except that then I do not see how a typical bishop (changing 2 co-ordinates as it moves) could possibly finish on its starting 2D board being just one diagonal step away from the square it started on, after visiting 3 different boards in 3 consecutive moves (in the single step fashion I described above) without the interconnection being in effect 4 dimensional. Perhaps a math wizard might try to explain it to a layman like me, if my conclusion is wrong. Meantime, here's a link to Directed Alice Chess III, followed by my test diagram for a possible 4D Alice Chess variant idea: http://www.chessvariants.com/index/msdisplay.php?itemid=MLdirectedalicei
[edit: my original idea to use four 2D boards for a 4D Alice Chess variant idea was to have it like Alice Chess as much as possible, but to allow up to 3 pieces of any colour to occupy any of a set of 4 corresponding squares (e.g. one set would be those with file & rank = a1). That's also with just the two kings additionally being allowed to take an enemy piece occupying any of the corresponding squares that they may move to on the way in finishing their move (thus a double capture move would be possible for a K), but then the only forcible 'basic' mate would seem to be K & Q vs. lone K, which is not totally satisfying for me.]