Some solutions with the first block increasing clockwise for 3 X 8:
..0..1..0..1..7..5..2..0....0..1..0..1..0..1..0..7....0..1..0..1..5..0..1..5
..3..2..3..2..3..4..3..5....3..2..3..2..5..4..5..6....3..2..3..2..4..3..2..4
..0..1..0..1..0..6..7..6....0..1..0..1..7..3..2..0....0..1..0..1..7..0..1..5
...
...R..L..R..L..L..R..L.......R..L..R..L..R..L..L.......R..L..R..L..R..R..L...
...L..R..L..R..R..L..R.......L..R..L..R..L..R..R.......L..R..L..R..L..L..R...
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