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  • $\begingroup$ Cool answer! Is there a non-symmetric version for knights? $\endgroup$
    – Dmitry Kamenetsky
    Commented Mar 2, 2020 at 23:51
  • $\begingroup$ "Pawns" seems to be solving a different problem to the others... for the pawns, many of them are "attacked" or "protected" by others of the same colour. For other pieces, they're divided into mutually-attacking pairs, where one of each pair could be switched for a black piece, and after any capture would not be attacking (or attacked by) anything else. $\endgroup$
    – Steve
    Commented Mar 3, 2020 at 14:02
  • $\begingroup$ @Steve yes this is the case but the pawns problem must be different as, if we stick with a single colour, there will always be a pawn not attacking any other pawn. $\endgroup$
    – hexomino
    Commented Mar 3, 2020 at 14:12
  • $\begingroup$ Yes, but the others could be converted to a solution where half the pieces are black... which would still not be the same as the pawns solution, because none of the pieces are "protected" by another piece the same colour (which is the same as "attacked" from the POV of the problem). If gaps are inserted to avoid white or black pawns protecting each other, there's only space for 42 on an otherwise-equivalent layout... $\endgroup$
    – Steve
    Commented Mar 3, 2020 at 14:21
  • $\begingroup$ @Steve Ah, okay I see your point, I can do a bit better than this I think so will edit in this alternative $\endgroup$
    – hexomino
    Commented Mar 3, 2020 at 14:22