user11144: 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...

user4418: Improving on Christian's answer:
    [Title "2 Black Pawns"]
    [FEN "1R6/p1p1P2N/P1P1P3/2P4B/P1P1P2N/6R1/3Q4/B4k1K w - - 0 1"]



user28283: 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:

11144: <p>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).</p>
<p>Working example (I placed stuff random):</p>
<pre><code>[FEN &quot;1K6/6NB/p7/3Q4/5R2/2R5/4P3/k3N1B1 w KQkq - 0 1&quot;]
</code></pre>
<p>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 &quot;fill&quot; a board). You <em>could</em> place a third knight on h8 but first try to get all White 8 pawns aboard...</p>
 4418: <p>Improving on Christian's answer:</p>
<pre><code>    [Title &quot;2 Black Pawns&quot;]
    [FEN &quot;1R6/p1p1P2N/P1P1P3/2P4B/P1P1P2N/6R1/3Q4/B4k1K w - - 0 1&quot;]

</code></pre>
 28283: <p>My final suggestion is this:</p>
<pre><code>[Title &quot;5 Black Pawns&quot;]
[FEN &quot;1Q6/5PNP/P1P2ppp/3R4/P1p4P/P1p2P1B/4R3/K1k3BN w - - 0 1&quot;]

</code></pre>
<p>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:</p>
