Thinking backwards here:
Black's previous move must have been ... b7-b5, to which White replied PxP e.p. (double and discovered check). Since White's light-squared B cannot move off the f1-a6 diagonal, White must have had some piece blocking that diagonal before Black played b5--white moved off the diagonal, giving discovered check. If we suppose it was the White K which was blocking the diagonal, then he was on d3
Therefore, the Black P currently on e3 was then on d4 (it took something on e3, giving discovered check from the Black Q). But the White K is in check by Black's B on h7, you protest, so the White K cannot have been on d3. Ah, but White once had a P on e2 which he played to e4 to stop that check; Black replied d4xe3 double & discovered check, resulting in the given P position. (The Black N was on f5, it moved to d6, opening up the discovered B check... but further back we need not reconstruct.)
Now, let us address the issue of what difference it makes whether White's flank P is on h3 or g3. If White has Ps on h3, g2 & e2, then the White R has no path to e6 (the light-squared B blocks the R). Therefore the position with a P on h3 is not legal. Whereas if the White P is on g3, the White R does have a path to e6 (up the open h-file); the upper position is legal.
Below is a probable position from which the puzzle position can be derived.
Black's light squared bishop must be a promoted pawn, since the pawn on d7 hasn't moved and the one on b7 has only just moved (Black's last move being b7-b5). This means that Black's original light squared bishop never moved and got captured on c8.
Hence one of Black's pawns must have reached b1, d1, f1 or h1. I have to go out for a while so don't have time to solve this fully, but I suspect that we can prove that the bishop on h7 must have been promoted on h1 and that only his h-pawn could have got there (there is a path via g3, but can any of Black's pawn reached there?). This would mean that position 1 is legal and position 2 isn't.
Originally posted by moonbusThis bishop could have left its original square and moved back, which would have created a path for the rook.
If White has Ps on h3, g2 & e2, then the White R has no path to e6 (the light-squared B blocks the R). Therefore the position with a P on h3 is not legal.
I'm not sure that we can even assume that the rook on e6 was the h1 rook, as both bishops could have moved and returned, the a1 rook could have gone to e6, and the h1 rook to a1.
That said, if we could show that the bishop on f1 has never moved, I think you'd be OK. I don't think we can, though.
SG's condition is that the position needs to be legal, but it does not have to be logical.
Originally posted by Paul LeggettI can't fault moonbus' reasoning, which leads to a sequence where the White e-pawn hasn't moved with the bishop on f1, still. Therefore, via the h-file is the only route for the h1 rook to get out, and thus the position with the pawn on g3 is correct.
This bishop could have left its original square and moved back, which would have created a path for the rook.
I'm not sure that we can even assume that the rook on e6 was the h1 rook, as both bishops could have moved and returned, the a1 rook could have gone to e6, and the h1 rook to a1.
That said, if we could show that the bishop on f1 has neve ...[text shortened]... h.
SG's condition is that the position needs to be legal, but it does not have to be logical.
Unless the rook on e6 can be a promoted pawn - then I have no idea!
Originally posted by Paul LeggettThere may indeed be multiple possible solutions, one of which involves pawn promotion. I accept that the White R on e6 might not be the original R from h1.
This bishop could have left its original square and moved back, which would have created a path for the rook.
I'm not sure that we can even assume that the rook on e6 was the h1 rook, as both bishops could have moved and returned, the a1 rook could have gone to e6, and the h1 rook to a1.
That said, if we could show that the bishop on f1 has neve ...[text shortened]... h.
SG's condition is that the position needs to be legal, but it does not have to be logical.
Can you show us an alternate sequence of moves without a White P starting at e2? If not, that is prima facie evidence that White's Bf1 has not moved.
Originally posted by moonbusI don't think it is a prima facie situation, in that the burden of proof lies with showing that the bishop has not moved. If we can't prove that the bishop has never moved, then we can't assume the rook is on e6 illegally.
There may indeed be multiple possible solutions, one of which involves pawn promotion. I accept that the White R on e6 might not be the original R from h1.
Can you show us an alternate sequence of moves without a White P starting at e2? If not, that is prima facie evidence that White's Bf1 has not moved.
I am merely saying that the bishops's presence on f1 does not prove that the rook on e6 is there illegally. Perhaps it is true, but right now it is an assertion not supported by evidence. My issue was with the original statement.
Originally posted by Paul LeggettI take your point regarding the question whether Bf1 has moved; lack of evidence is not evidence of a lack.
I don't think it is a prima facie situation, in that the burden of proof lies with showing that the bishop has not moved. If we can't prove that the bishop has never moved, then we can't assume the rook is on e6 illegally.
I am merely saying that the bishops's presence on f1 does not prove that the rook on e6 is there illegally. Perhaps it ...[text shortened]... ght now it is an assertion not supported by evidence. My issue was with the original statement.
My proposed solution makes some assumptions. A) That SG's OR is logically exclusive. That is, only position 1 is legal, or only position 2 is legal, but not both. B) That neither White rook is a promoted pawn. I have not assumed that only one solution is possible, and if assumptions A) or B) (or both) be challenged, then other solutions might well be possible.
If assumption B) is challenged, then Rh1 does not require an exit path. If at least one of the White rooks is a promoted pawn, then the Bf1 need not have moved in order for White to place a rook on e6; but in that case, neither is it needful to open the h-file (i.e., position 1). The original White Rh1 might have been taken by a Black piece or by Black's h7 pawn, and the rook currently on e6 is a promoted pawn (or it is the a1 rook, and the rook currently on a1 is the promoted pawn). This scenario does not distinguish between the legality of position 1 and position 2--that is, both might be legal. Therefore, rejecting assumption B) also seems to require rejection of assumption A). But if both position 1 and position 2 are legal, why bother to pose the puzzle?
I point out in passing that FatLady is probably correct that the Black light-squared bishop must be a promoted pawn, because b7 and d7 have not moved. It cannot however have promoted on h1. Although it might have arrived there even if White had a pawn on h3 (by taking White pieces on g3 and h2), it could not have exited the corner on account of the White g2 pawn. It is unclear whether this has any bearing on whether position 1 or position 2 is legal. Open for further discussion.
This is the legal one.
The H7 Bishop is a promoted piece.
The h7 pawn must have promoted on d1 to a Bishop.
All the other Black pawns can be accounted for.
The pawn on e3 is the Black c-pawn it came from d4 after the ep capture.
You cannot get a pawn from h7 to d4.
White has lost prior to the ep capture five men.
One capture by the c-pawn to get to the d-file.
The h-pawn took on g6,f5,e4,d3 (that is the total of five captures)
and then moved d2-d1 = Bishop.
The pawn was on e2 prior to playing e4 and allowing the ep capture
so the f1 Bishop has never moved.
The 5 captures indicate White never promoted a pawn so it is the
original piece.
The h1 Rook must have got out after hxg3.
I think that's it, but as always I've probably overlooked something obvious.
Originally posted by moonbusThat seems very well-reasoned to me!
I take your point regarding the question whether Bf1 has moved; lack of evidence is not evidence of a lack.
My proposed solution makes some assumptions. A) That SG's OR is logically exclusive. That is, only position 1 is legal, or only position 2 is legal, but not both. B) That neither White rook is a promoted pawn. I have not assumed that only one soluti ...[text shortened]... this has any bearing on whether position 1 or position 2 is legal. Open for further discussion.
Originally posted by greenpawn34SOLV'D.
This is the legal one.
[fen]6N1/p2prppb/kP1nR3/3qp3/8/2K1p1P1/1P4P1/R1B2B2 b - - 0 1[/fen]
The H7 Bishop is a promoted piece.
The h7 pawn must have promoted on d1 to a Bishop.
All the other Black pawns can be accounted for.
The pawn on e3 is the Black c-pawn it came from d4 after the ep capture.
You cannot get a pawn from h7 to d4.
White has ...[text shortened]... out after hxg3.
I think that's it, but as always I've probably overlooked something obvious.