black has captured a piece or e-pawn on a6 - as white has not promoted any pawn, it must be a bishop or a rook or e-pawn. But white has already a white-sq bishop, so it must be white's rook or e-pawn.
can it be e-pawn? for that white needs to capture 4 black's pieces (g-pawn not possible) - black has only 2 pieces and 1 pawn missing. There it was not e-pawn that was captured on a6 - so white's other rook must have been captured on a6.
Therefore it must be black's queen rook on a5.
Not much to add to this -- nice work dsarkar.
Curious that White's Rook got out to get captured -- another "pawn swap" situation maybe? It may be in there as a red herring, when the solution's actually much more straightforward.
Something seems wrong... dsarkar's analysis is completely correct, but this seems too easy. I mean, there's some trickiness as to how the white rook escaped, but furthermore trickiness as to how the a2 bishop got there. Yet none of this, nor (and this is the biggest thing contributing to my sense of trepidation) the given information that black has just castled, is necessary nor even helpful to know.
Wait...
"white has no promoted piece in play" - does not reject the possibility that white had promoted e-pawn through g or b hole, and it was captured.
"black has just castled" - meaning if white's e-pawn promoted through g-hole - it had not given check to move the K or R.
I did not consider these...
Black's two bishops are of the same color - meaning black MUST have promoted g pawn thru e-pawn hole!
g-pawn had made 3 captures to promote - only 3 white pieces/pawns missing - meaning white did not promote e-pawn.
no, puzzle is not wrong - my original assumptions might be wrong!
Wait...
"white has no promoted piece in play" - does not reject the possibility that white had promoted e-pawn through g or b hole, and it was captured.
"black has just castled" - meaning if white's e-pawn promoted through g-hole - it had not given check to move the K or R.
I did not consider these...
Actually, white's e-pawn could have promoted on the c-file via dxc7. Similarly, black's g-pawn could have slipped through to g2 via fxg2, OR to h2 via gxh2 (while white's g-pawn was still on g2), which requires significantly fewer captures. It appears all is not solved yet...
ok - black's 4(-1?) pieces/pawns are missing - white's 3(-1?) pieces/pawns are missing.
We know black must have promoted - we do not know yet whether white has promoted (and the piece got captured) or not...
if black's g-pawn slipped thru gap, it made at least 1 capture to promote to h1
promotion-capture must be a piece - a6 - capture must be a piece = at least 2 white pieces (or 1 piece+ 1 promoted pawn - not pawn per se) were captured by pawns
white piece captured on a6 was either a rook or promoted piece - cannot be a black-sq bishop.
white piece captured by promoting g-pawn must be a black-sq bishop, rook, or promoted piece.
so white pieces captured were (1) black-sq bishop (2) rook or promoted piece.
if white promoted at all, e-pawn made at least 2 captures.(candidates are black-sq bishop, rook, queen).
So there is no more confusion, here's how to achieve the position from the starting position.
it must be blacks queenside rook. Note that the e-file isn't usable, because if you promoted a bishop there, it would get stuck.
The black Q-rook cannot have come out before a6-capture
(1) if a6-capture was a promoted white piece, then white e-pawn could not have captured black rook (rook could not come out before a6 capture) - meaning it must have captured Q and black-sq bishop
(2) if a6-capture was white rook, then g-pawn must have captured promoted piece. that means white promoted earlier.
I think a paradox exists regarding who promoted earlier...
MBickley, I get your point. But how do you eliminate white's promotion of e-pawn? "white has no promoted piece in play" - does not eliminate white's promotion.
Ok (I double and triple checked this one!).
On square a5 there is a Rook, of unknown color. With the knowledge that a)White has no promoted pieces in play and b) Black has just castled, which side does the castle belong to?