Some solutions for n=5 k=3
..0..1..0..0..1..0....0..1..0..0..1..0....0..1..0..0..1..0....0..1..0..0..1..0
..2..1..1..1..1..2....2..1..1..1..1..2....2..1..1..1..1..2....2..1..1..1..1..2
..2..0..0..0..0..2....2..0..0..0..0..2....2..0..0..0..0..2....2..0..0..0..0..2
..0..0..1..1..0..1....0..0..1..1..0..1....0..0..2..2..0..1....0..0..3..3..0..0
..3..3..1..1..0..1....2..2..1..1..0..1....1..1..2..2..0..1....1..1..3..3..1..1
..0..3..0..0..0..2....3..2..2..2..0..0....3..1..3..3..0..0....2..1..0..0..1..0
..0..3..0..1..1..2....3..0..0..2..2..2....3..1..3..3..1..1....2..1..0..0..1..0
..3..3..0..1..1..3....2..0..0..1..1..1....1..1..2..2..1..0....1..1..3..3..1..1
..1..1..0..0..0..3....2..1..1..1..2..2....0..0..2..2..1..0....0..0..3..3..0..0
..0..1..3..3..0..1....0..1..0..0..2..3....2..0..3..3..1..2....2..0..2..2..0..1
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