Even more fun facts: if you change the problem instead to 4 queens and one knight, there is exactly one solution up to symmetries (rotations and flipping). Here it is:
..N.....
........
........
....Q...
.....Q..
...Q....
......Q.
........
Edit: even more fun facts: if we take the standard piece values of Q=9, R=5, B/N=3, then we can ask for the smallest piece budget that attacks every square. The cheapest possible configuration is 24 points, you can see one with 8 bishops: ........
....B...
....B...
.B......
...B.B..
.....B..
..B.....
....B...
Which has pleasing symmetry when you view it as a composition of light-square bishops and dark-square bishops.
wow. oddly that seems like an easier problem, despite the solution space being smaller. not saying i woulda solved that, because i doubt it, but it’s much closer to what my raw intuition woulda spit out as a solutuon to the OG problem.