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Place the whole army of White and the black king on the board, such that no piece is attacked or defended. (Obviously you must use double pawns.) That's fairly easy, so tie breaker will be how many black pawns you can additionally smuggle in (again no piece being attacked or defended).

Working example (I placed stuff random):

[FEN "1K6/6NB/p7/3Q4/5R2/2R5/4P3/k3N1B1 w KQkq - 0 1"]

As you can see, no more remaining White piece fits on the board (pawns on 1st/8th are illegal - please only legal positions, otherwise 32 knights would be the way to maximally "fill" a board). You could place a third knight on h8 but first try to get all White 8 pawns aboard...

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  • You already accepted, so I don't know whether you'll still check it, but actually I found another solution :)
    – Christian
    Commented Dec 15, 2022 at 15:12
  • I don't, but since I get auto-alerted to messages, I now know :-) (P.S. Unbelievable. 10 BP are an obvious hard maximum by row/col, now subtract diagonals - 3 with Q in the corner - and I think we are so >< close proving 5 pawns are indeed optimal.)
    – Hauke Reddmann
    Commented Dec 16, 2022 at 8:36

2 Answers 2

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5

My final suggestion is this:

[Title "5 Black Pawns"]
[FEN "1Q6/5PNP/P1P2ppp/3R4/P1p4P/P1p2P1B/4R3/K1k3BN w - - 0 1"]

After letting my first program run for 20 hours and checking around 1.5 billion positions without finding another pawn I added a small improvement by defining the Queen's position explicitly and resigning on branches a bit quicker and - et voilà - after like three minutes of searching it found this solution:

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  • 1
    The second diagram is much less good than the first or the third, because both bishops are on light squares, and this (plus the 8 pawns) makes the position illegal.
    – Evargalo
    Commented Dec 14, 2022 at 14:15
  • 1
    Wow, thank you for the hint. I didn't even realize.
    – Christian
    Commented Dec 14, 2022 at 14:17
  • I'm utterly surprised that Q and one B are not on the rim. P.S. I put the accept on hold in case your program finds a fourth. :-)
    – Hauke Reddmann
    Commented Dec 14, 2022 at 16:54
  • Yeah - me too actually. Now I put some small optimization to look more for places for the pieces I guess are more likely to provide a solution and both bishops and the queen are on the rim ;) I'll continue to let it run tomorrow, but if until 4pm there is still no better solution, I think I'll have to quit it.
    – Christian
    Commented Dec 14, 2022 at 21:40
3

Improving on Christian's answer:

    [Title "2 Black Pawns"]
    [FEN "1R6/p1p1P2N/P1P1P3/2P4B/P1P1P2N/6R1/3Q4/B4k1K w - - 0 1"]
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    Haha, nice - that is what you get for writing software to come up with a solution and then not even taking two minutes to look over the solution :D
    – Christian
    Commented Dec 13, 2022 at 16:19

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