Deductive Puzzle #39

Black's Queen Bishop is invisible!

Know the following:

a) White gave black odds of a Knight in this game.

b) White hasn't moved his king.

c) Not more than one piece was captured on its own squares, and it was not the first one captured.

With this info, is the invisible Bishop still on the board, or was it captured?

a little shameless self promotion...

there are 8 black pawns. only piece to get to a3 is the black bishop (queen and 2 knigthts are still there), so therefore it was captured on a3.
this ones got a fault in it? or is it supposed to be this easy this time?

That's Black's King's bishop that was captured on a3, not the Queen's bishop.

 no, black's queen bishop is light-squared..

Because we know that White started with only one Knight it must have been the Queen that was captured on f6 to free Black's King-side Bishop.  Because we know that White's King hasn't moved (to provide a King-side avenue of escape for the Queen) the c3 pawn push happened before White's Bishop was captured and therefore it must have been captured either on it's starting square or b2.  The Queen's capture must have been the first capture of the game since any other prior capture would have required a piece to have been captured on it's starting square by a Knight.

After this Black's King-side Bishop was captured on a3 and the Rook escaped to be captured on a6.

But how did White's Rook get out?  It must have moved while the Knight was off of b1 and (before the a3 capture because that would have then been the only way back to b1 for the Knight).  In order to do so it must have moved to either c1 or d1 meaining that the Bishop was gone, and since the b2 pawn would still have been there White's Queen-side bishop msut have been captured on c1 before the rook moved over.  then, once the Knight was back on b1 and the capture took place on a3 the Rook was free.

But what does this all tell us about Black's Queen-side bishop?  It tells us that it wasn't the peice captured on it's starting square, and it also couldn't have escaped from that square before the Rook was captured on a6.  Once the rook was captured, all of White's remaining peices were tied up and none could have possibly captured the now-free Bishop therefore it must still be on the board.

That's so I don't spoil the solution for others who might want to solve it.  Highlight the text and you'll be able to read it.