The missing piece

Another problem of The chess mysteries of Sherlock Holmes by
Raymond Smullyan:

I'll shorten the story.
Sherlock Holmes enters a room and sees a chess-set with a shilling
on h4, representing a missing piece. He is then challenged to deduce
what the missing piece is. Of course he succedes.

White: Kh8, Rd7, Rd8, a5, b4, c3, d3, e2, g3, h2
Black: Kb7, Na1, Nc8, a6, a7, c4, c5, d6, e7, g7
h4: a shilling, representing the missing piece

Who can tell me what the missing piece is?

Do we have to assume that both players played sensibly?

Sensibly I don't know.
They played according to the rules of chess, so this position can be
reached playing from the begin-position.

Obviously, it is Black's move, but is there anything else we need to
know to solve this? I'm stuck, since I don't see any way to prove that
one piece is any more correct than any other. (Except that it cannot be
a Black Rook or Queen). Also, how is it that white was able to move
the rook to d7 with check? It could only have come from c7, where it
would still be checking the king. I don't see that any piece on h4 could
fix this issue.

What am I missing?

Rein

Did the rook on d7 really come from c7?
Or did white play another last move?

To answer your question if you need to know more: no! You've got all
the information you need to solve this problem!
I must say it's rather complicated...

sorry - entered.
White's last move could have been cxd8+ promotes to rook.
but then...
Gil

What did the pawn capture?

didn't figure it out yet. But the missing piece is NOT a white pawn.

going ahead slowly: i think it was a bishop:
- 2 knights still on the board
- with Queen or Rook white would be in check before and after blacks
last move

later , i am going to reason further from there....

Is this the way the board was set up?

http://hometown.aol.co.uk/rhymsta/Puzzles.html

I think that's what Hotpawn said - thanks Andrew! Colin

Yes it is.

Thank you very much, Andrew!

Otto

are you sure the missing piece is on h4 and not on h3?
I seem to be stuck somewhere. Sin.