Scott Purdy sent me the problem below.
The answer to this is:
xxRNxxxR
xPPPBxPx
PRBxQxxx
PxPxxxNB
xBxPxxRP
xNxxPxPx
PxPKxNKx
QPxPxxPx
Here's how I solved it (maybe not the most efficient way)
First, pawns can only be attacking N, R, or other P. Eliminate the ones
that are only attacking Q, B, K, nothing, or pieces you have already
eliminated. This eliminates 8 pieces.
Next, there is a King which is attacking only pieces which are attacking it
(or blank space). Remove it.
This leaves the 2 Kings remaining. Eliminate mutual attacks around them.
Third, a Queen must be under attack by a N. Otherwise it would be a mutual
attack. So eliminate the two Queens not under attack by N. (now we know
where the two queens are and one of the knights is)
Eliminate the pieces around the Queens which cannot possibly exist and we
clear a little more space.
Eliminate another pawn which isn't attacking anything.
There is nothing that can possibly be attacking the R at h6, so eliminate
it.
Now look at the 5 bishops remaining. The ones at D6 & E7 could not possibly
both exist. Therefore the other 3 bishops are real. In fact, that proves
that the one at D6 could not be real because of the possible pawn at C5.
We can eliminate a couple more pawns.
There are 6 R left. There are 2 pairs of Rooks attacking each other: A8/C8
and H6/H8. Only one of each pair can be real, which means the other 2 Rooks
are definitely real.
At this point we have 16 pawns remaining. All real.
Every pawn has to be attacking something, so make real pieces in front of
the ones that are only attacking one unknown piece.
Knights can't attack real knights so get rid of the fake ones.
The end.
-Jay