Deductive Puzzle #13

As you can see, the only missing black pawn is that from b7. Has he been captured, or did he promote? Know that White IS able to castle.

White's b-pawn must have made a capture on c3, and Black's only missing peice is the b-pawn.  It must have captured over to the c-file in order to be snapped up on c3.

Surely it's not so simple?

Unless it both promoted and was captured....

What's odd is that the White bishop must have escaped via the b-file after the capture, and becuase the King can still castle the missing Queen and Rook would have been locked in so how did the pawn get to the c-file in order to be captured there?  Surely not by capturing the missing h-pawn....

The b-pawn must have captured to the a-file from b3 by taking the rook, promoted and been subsequently captured on c3.

The only other potential complication is the possibility that White's h-pawn promoted via a black "pawn swap" on the g and h files in order to get over to the c-file to enable the capture and prevent the need for the b-pawn to have promoted.  One piece (either the missing Queen or Rook) would be required to allow the pawn through via the clearance of the h-file, and we know that neither could have possibly escaped prior to the capture on c3, so this is not a possibility.

[Edit: Er, minor point of clarification -- another peice could have been captured on g3 and the h-pawn promoted into a peice of the same type.  Candidates are a light squared Bishop or a Knight.

The problem, though, is that it would still be missing as whatever the Pawn promoted into would also need to have been captured on the c-file meaning that four captures would be required (The Queen and Rook being neither candidates for g3 or c3) but only three white peices are missing.  The sequence described earlier must be the solution]

TheGrobe:

If we are assuming the White dark-squared Bishop is an original piece, then the capture on c3 had to have occurred before the pawn advance a3 so that it could get out, which means that the b-pawn did not promote by capturing the Rook on a2 before getting captured on c3.

Also, if said Bishop is a promoted one, then one of the three missing White pieces had to have come through the opening on the b-file (to allow for the captures on g6 so that promotion could occur), so again the capture on c3 would have had to have been done before the pawn advance to a3.

Now, if we consider that one of White's Knights may be a promoted piece, then it is possible for the promotion to have occurred before the capture on c3. However, if the h-pawn promoted on h8 after hxg6 (Black is only missing one piece, so the pawn on g3 is the g-pawn), then the Knight could not have escaped from h8 without capturing another pawn.  The only other possibility is that the pawn captured a piece on g7 behind the g-pawn in order to promote on g8.  This piece would then be replaced by the b-pawn's promotion. If this occurred, however, then what was captured on c3?  We have one capture too many, here.

if black promoted, white's dark-sq bishop could not have gotten out, so white's dark-sq bishop must be promoted, and all others pieces are original. So if black promoted, white must have also promoted(dark-sq B). Or none promoted.

If white promoted, it cannot have made any capture (only 1 black pawn/promoted-piece missing) - so it promoted to h8. Before that, black must have captured something on g6 by h7xg6, his rook came out, white promoted to black-sq bishop, black captured some white piece on h6 by g7xh6, then white's black-sq bishop came out.

if either=both promoted, all pieces except white's dark-sq bishop are original.

White is missing only Q,R and h-pawn-OR-dark-sq-bishop.

if either=both promoted, black's b-pawn must have captured a-R at a2.

That means only Q was available for first capture at g6 - a white sq. 

That means if either=both promoted, black must have promoted first, as before black's promotion, white's Q could not have gotten out.

As black promoted first, white's a-Rook, dark-sq-Bishop were captured before getting out. so only one white piece is available for capture at the g-h complex, not two, which is not possible.

Therefore my original supposition that either=both promotion has occured is wrong. Neither has promoted, and the black b7-pawn was captured on c3. 

I think I see what you're saying -- the only candidates for capture on the c file are the light squared bishop or one of the knights.  Once this capture was made, the rest of the peices could have flooded out to enable the capture on g6 that allowed the h-pawn to promote -- but it could only have promoted into the peice that was captured on the c-file, so we can deduce with certainty that the dark-squared bishop on h4 is the original.

The problem with this is that the pawn couldn't have promoted to a light squared bishop without capturing to g8, and there are not enough missing black peices to support this.  If it were promoted to a Knight, the knight could never have escaped (as there were, and still are pawns on f7 and g6 that would have had to have been captured to allow the Knight out) and would either still be on h8, or would be missing from the board having been captured back there.

As a result, the sequence I described above, where the b-pawn captured the Rook on a2 from b3, promoted to a Queen or a Knight and was subsequently captured on c3 is the only possibility.

One final possibility I'd not addressed:

The h-pawn could have been captured, the h1 rook escaped to be captured on the c-file and to be later replaced on h1 by the a1 rook after its escape.

Thankfully, this is simple to refute as we know that this can't be the case having been told that White can still castle meaning that the h1 rook is the original.

Sorry Grobe, but you don't have the correct answer there.

WARNING: DON'T GO THROUGH THIS GAME IF YOU DON'T WANT TO SEE AN ANSWER!

Probably could have been done in less moves but I was just going for the final position. 

I need to just double check, but I think we may have a winner :)

The capture of a black officer on c3 preceded the pawn promotion, which in turn replaced the captured piece :)

Hmmmm, I can't see how it could have happened any other way.  The only White peices out before the capture on c3 could have been the Knights, the light squared bishop and the h-pawn.  The Knights or the light squared Bishop could have been captured on the c-file, but would then have needed to be replaced by the promoted h-pawn as they all appear to be on the board, and I've shown that this can't be the case as promotion to a light square Bishop requires a capture, and the Knight couldn't escape after being promoted on h1.

The Knights or the light squared bishop could also have been captured on g3, but again would need to have been replaced and this poses the same problems.

I think I've missed the possibility that White's dark squared bishop could have been captured on its original square allowing the Queen out via a2 prior to the c3 capture.  This would have allowed a capture on the c-file (Queen), the capture of the Rook on g3, the promotion of the h-pawn to a dark-squared Bishop and an escape path for that Bishop opened up by a capture of...

...what could have been captured on h3?  There are only three missing white peices.

It's a demonstration of how if could have happened, but I'm struggling a little to understand though why the White Rook couldn't have been captured on a2 by the b pawn and subsequently captured on c3 allowing the Bishop and Queen out.  Surely there must be a reason, but without it I don't know that it's definitively solved.

With pawns on a3 and b2 or c3 white's dark squared bishop has no way out. That is really the final key, you need to figure how white got his dark squared bishop to h4. 

Yes -- gotcha.  I'd missed that.

Thanks, bondiggity.