Bishops - 7?
Queens
- 8, believe it or not. The Queens have to be placed a knights move away from the other. I started on h1 (not h8, as diagram stated) and filled in 7. Last queen is on the square that is not controlled by rank or file by another Queen. i.e. the only safe place for a king when you have 7 perfectly-placed enemy queens on the board. STALEMATE!
Knights - They always have to move from one colour to the other - ie. from light to dark, or from dark to light. So, that makes it 32.
Pawns - That's easy. Fill each rank OR file alternately with pawns and that makes it 32.
Kings - Every 2 ranks or 2 files = 4 kings...so 16 kings.
...each other? For the rooks, it is easy, but what about the others?