Careful, the site sometimes warns people for 5+ consecutive posts lol
But yeah the Queen can move any number of cubes in all 26 directions, which ends up being 86 cubes in total (from a central position).
I wonder how many queens it would take to force checkmate (not just a checkmating position) but actually able to force the long king from the center to the face/edge/corner of the board.
In fact just looking at the kings and queens for now is the best way to start discussing 3d chess because there's no argument about how the piece movement should be scaled up to 3d. King, one cubes in any direction. Queen any number of cubes in any straight line direction, just like 2d chess, simple. 2 queens can checkmate a king in the center with this well known pattern:
How many queens would be needed for a similar pattern in 3d where the queens have to cover 26 different cubes this time!
2 probably
Bishops can do straight but into other boards and its pretty fun to use them
Its actually fun irl, 3 boards are more than enough with 1 set
Nah that's not real 3d chess then, board should always have equal dimensions in every direction.
You would need 4 3D queens. One below the king, 2 in a diagonal relative to the one below, one in a triagonal.
I'm trying to visualize that it is so hard lol, so if let's say the lone king in on the 5th level, on e55, would this configuration of queens be checkmate?
Level 5:
Level 8:
IF you want ez 3d viasualizing, set up 3 boards, one for each spatial dimension, then you'll see.
More like this:
Level 1:
Level 2:
Level 3:
Yes the queen directly below the king covers all the cubes in two of the levels of movement, and then 3 queens are needed to cover the top level of movement, wonder if this could be reduced to 3 queens total?
(1,0,0) + (-1,2,0) + (-2,-1,0)
Those are the coordinates relative to the king?
(1,0,0) + (-1,2,0) + (-2,-1,0)
This position does indeed counts as checkmate
Now how many queens required to force checkmate is the next question!
I suspect that 2 Queens would be enough, with the help of their King. Even 3 Kings (only one of those royal) might be enough. This based on the fact that on 8x8 in 2d two Kings can easily force mate, by some kind of pincer movement, one King blocking escape from the corner along a file, the other along a rank. So it seems one needs one King per dimension.
What do you mean by two kings?
And a rook can go to any other layer in the game