Some solutions for n=3
..0..1..1..0....0..2..2..2....0..0..0..0....1..1..2..2....2..2..2..0
..0..0..0..0....0..1..1..0....0..0..0..0....1..1..2..2....0..2..2..0
..0..0..0..0....1..1..1..0....0..0..1..1....0..1..1..1....0..0..2..2
..1..1..0..0....2..2..2..2....0..2..2..1....0..1..1..1....0..0..2..2
|