The missing piece

Yes, the missing (white or black) piece (pawn,knight,bishop,rook or
queen) is on h4.

Otto

OK let me try the solution. Is it ok?

1) white's last move was cxd8+ promotes to pawn
black was not in check before the move, so there had to be
something between d7 and b7, can only be the pawn promoting

2) which piece on d8 was taken?
Not queen or rook. Could only be if black's last move was to put it
there with check, or take one in between d8 and h8 away, both
impossible.
So it is Knight or Bishop.
If knight, then it's a promoted piece (2 others there)
If bishop, idem, because the bishop on f8 (the other black square
bishop) cannot have moved (e7, g7 still there).

Hence, black has promoted a pawn

3) It is not a black piece on h4
Rook or queen are impossible. White could not have made cxd8+
while being in check!
The knights are there.
The black square bishop has not moved/was taken on f8
The white square bishop is on the wrong color
All his pawns are there, except the one that promoted

4) which white piece?
not a pawn (they are all there before the cxd8)
black has taken 1 piece with b-pawn
black has taken 3 pieces with f-pawn to get on c4
black has taken 1 piece to get on g2 (hxg2)
(promotion could not be through f-file because that would require one
more capture, impossible see below).

total 5 pieces out of 6: 1 Q, 1 R, 2 N, 2 B
only one piece not taken by a pawn

all takes by white pawn were on white squares (that's why g2 is
important)

leaves only white's black-square bishop


Solution: white bishop on h4.

sin

Congrats!! Well done.
This was a difficult problem, although I have more difficult problems
like this.
Your reasoning is perfect except for a minor detail and what I think is
a typing error.
Minor detail: The piece taken on d8 can be an original knight, it
doesn't have to be the promoted (and it can be a bishop as you
demonstrated).
Typing error: All the white pieces are taken by black! pawns, all on
white squares.
This was a retrograde-problem.
Most of the chess-problems are about determining what must be
done in the FUTURE of the game.
Retrograde-problems are about determining what has been done in
the PAST!

Thanks. And yes, both your remarks are correct.

I was in trouble before because I thought the h-pawn had infiltrated
through the f-file. And therefor had at least taken twice (once on a
black square), leaving no white pieces.
In that case the only solution was black's white-square bishop, but
that was on the wrong color. That's why I asked about h3.
Your answer made me look again, and then I saw the promotion
through h3 - g2, leading to the solution.
Sin.