Deductive Puzzle #14

The a7 pawn has promoted! You know that both kings have only moved once. Which black piece has the a7 pawn become?

The black pawn must have captured a white piece - one of the two missing white rooks - and moved to the b-file.

Also, both kings are two squares away from their starting positions, so their only move has been castling.

Important: Is the promoted pawn still on the board?

... which piece has be become... if it wasn't on the board, this would be a pretty existential question :p

Just checking

Well, here's a sample game I started as an attempt to find an answer.  It doesn't work, though, since the pawn has no piece it may become: there is no black queen, the rooks are accounted for and a rook would check the king anyway, and both a knight and bishop would check the king as they tried to leave the corner, forcing a capture or second king move.  Maybe it'll still help somehow.

EDIT: A light bishop could escape from the corner.  However, the pawn's promotion on the light square requires it to pass through b2, where it would check the king.  It couldn't promote before the king castled, either, since with the king on e1, the other rook couldn't leave the kingside to be captured by the a-pawn...

(Am I the only one working on this?)

Well, here's what we do know:

• Both sides are missing 2 pieces.
• Both sides have castled.
• Both black rooks must be original.  The only way for either rook to leave the edge would be if the g- and h-pawns switched files, but that in itself would take two captures, leaving the a-pawn unable to move to the b-file.
• Therefore, the pawn must have promoted to either a bishop or knight.

A relative sequence of events:

1. Something (the queen or the piece to be replaced) is captured on c3.
2. White's dark bishop leaves the back rank.
3. White castles.
4. One of the rooks is captured by the a-pawn, bringing it to the b-file.

This one is difficult and I am thoroughly stumped for the same reasons posted by arc64...though I will not give up yet....

Two white pieces have been captured - one or both by a7-pawn. As white has not promoted any pawns, the captured white pieces are his 2 Rs. And queenside rook was captured after white castled. 

Two black pieces have been captured - one on c3. As the black rooks have not left the back rank, piece captured on c3 can be either of the 2 Ns, black-sq B, or Q.

Alright, I definitely need a hint on this one. So this is what I have thought out so far.

For Black's pawn to be able to promote, it has to capture something to get around White's a-pawn. This is true because White's a-pawn must be original, since the b-pawn must be on c3 and couldn't have became the a-pawn. 

So black must capture something. White has only 2-pieces missing and those are both his rooks. This combined with the fact that White's king must only move once results in White needing to castle before any promotion can be considered. With the king on e1 and pawns on f2, g2, and h2 the h1 rook can't escape. Also the only way to get to c1 in one move is by O-O-O so the a1 rook can't move either. 

So now white castles, which can only happen if the capture on c3 is made. This is true because there is no other way for the dark squared bishop to be let out. White can either capture black's queen, or the piece that the promoted pawn will replace. 

So now white castles and moves his rook to offer it as a sacrifice to the black a-pawn so it can get in range for promotion. However black can't promote on the b-file since b2+ will result in the king moving or a second time! Therefore white must offer up his second rook so that black can promote on the a-file. 

So now black has four options of what piece to promote to, but none of those seems logical!

Queen - With no Queen on the board this is obviously not the piece.

Rook - No way for black to get the rook back onto d8 or e8 without movement of the king due to the pawn structure. 

Bishop - Dark squared bishop, can't on a1-h8 diagonal because c3 is blocked. Would have to maneuver from a1-b2-a3-c5-d4-f6. However moving to b2 causes check! White must either move the king or capture and neither is an option!

Knight - Same as the bishop, there is no way for the knight to logically escape. b3 is check and a king movement or capture must occur. c2 would capture the pawn which is needed for the final position.

In conclusion, I am definitely missing something. 

No, you definitely aren't. I was. I just read your post and was like WTF!?!? So went back to check the diagram. It is now fixed.

Since there IS a black queen, that must be the piece it promoted to.

Oh well that is a boost to my intelligence :D. Its the queen. Place the white bishop on b1 so the promotion doesn't come with check. a1-a2-c4-c6-d7. The capture on c3 was of the black queen. 

My take on it, at a glance, makes it appear that the piece is a Queen.

A black piece has been taken on c3 and replaced by promotion - I can't see any other possibility. The pawn had to promote on a1- if it promoted before White's castling there was no piece it could have taken to get to the b-file, but for it to promote elsewhere it would have checked on b2 and forced the King to move again. It can't have promoted to a Rook because both Rooks are present and they can't have gotten there from a1 without the black King moving. A Bishop or Knight couldn't have escaped without checking or taking a pawn. This leaves the Queen.

EDIT: Oops, bondiggity beat me to it!

Also, I absolutely love these puzzles. Can you tell me the name of the book, I would definitely be interested in acquiring it. Also an extreme thank you for posting these!

It must be a Queen or a Knight -- here's why:

The only missing black piece was captured on c3, so we know it was not the light-squared Bishop, which could not have been captured on a dark square.

Because black has captured, and based on Black's pawn structure neither of Black's Rooks couldn't have escaped without a "pawn swap" on the g and h files, requiring two captures, but a third is required for the pawn to get past White's a-pawn to promote.  So we know the two Rooks are the originals and it did not promote to a Rook.

If the pawn was promoted to a dark-squared Bishop it would have had to have promoted by capturing White's King-side Rook on c1 prior to White castling, as its need to escape via a3 would have put the castled White king in check.  Because, however, before White castled the a1 rook had to remain on a1 (in order to still be able to subsequently castle ), the only piece that could have been captured to allow the a pawn to get to the b-file was White's King-side Rook which could not have subsequently also been captured on c1.  Because of this it is not the dark-squared Bishop.

Adding the black queen totally changes the problem. Now black has 1 missing piece - white two Rs (original). White has not promoted.

If black promoted first, and then there was c3 capture of the promoted or its original equivalent piece - which means black captured a rook first to go to b-file, then captured again to slip into gap of a3-b2 pawn to a2 sq, promoting to a1 - but that is impossible (QR captured after castling, castling could not have occured before removal of white's QB, and that could not have come out before c3-capture).

bondiggity and SirDavid,

I do not follow your logic when you say a7-pawn got promoted to a1.

Ahh, yes, because the Queen-side rook can't have gotten out on the e file before White castled the promotion must have occurred after castling (in order for the pawn to have been able to capture over to the b-file), and furthermore, the pawn can't have come in via b2 without Checking the castled king.  this means that the pawn must have captured back to the a-file by taking the second rook on a3 and promoted on a1.

If it had promoted to a Knight, it would have had to have escaped via c2 (which still has the White pawn on its original square), or via b3, which would have checked the castled king so it could not have been a Knight.

Based on the possibilities I excluded above and this the only possible answer is that the pawn was promoted to a Queen via the following sequence:

1. Black queen captured on c3 by White's b pawn
2. White's dark-squared Bishop (and Queen) escape(s) via the hole in the b-file
3. White castles
4. One of White's Rooks is captured on b4, b5 or b6 by Black's a-pawn
5. The second of White's Rooks is captured on a3
6. Black promotes the pawn to a Queen on a1 while some peice blocks the check along the first rank
7. Black's new Queen escapes out the hole in the b file

I should note that in the sequence described above, both of White's Rooks escaped via the e-file to come back around and be captured over on the Queen-side.

"Chess Mysteries of the Arabian Knights" by Raymond Sullyan. Fought it for a buck at a used book store. He also did 'The Chess Mysteries of Sherlock Holmes" which I will be putting up after I get through this one.

Read my lengthy post, #11 where I reasoned it out before the addition of the Queen showed that in the current state there was no solution.