Deductive Puzzle #5

Ok, so for todays Puzzle, imagine there is a big Question Mark on g4! This is because there should be a piece there! The question at hand it, what piece is there and of what color is it? Furthermore, can Black castle?

Well so far the people posting the correct answers have been posting it for me and I just need to say "you're right!" But if no one gets one of these, I certainly will explicate the thought process needed.

Hard to answer, since Black has a white-squared bishop which could not reach the position it is in through any sequence of legitimate moves . . .

But the question, "Can Black castle?" suggests that it is a white rook or queen (in which case the answer is "No".).  I'll need to think about this some more - gotta go see "Wolverine" now . . .

I disagree. Blacks e-pawn could have captured its way over there, and captured a piece on b2 while promoting to a white-squared bishop. So there! 

Can't solve the puzzle though.

Well, all I know so far is that the piece on g4 is not another White bishop.

The first thing to look at is the white pawns. Those on b2, c2, and d2 can't have moved, which means that the b3 pawn must have captured something and began on a2. This means that the bishop on a2 can't have gotten into that position from outside the pawn chain, which must mean it was a promoted pawn. The only light square available for this to happen on is b1. Now, what must have happened for that is that the black pawn starting on e7 captured white pieces on d6, c5,b4, and a3 successively, moved to a2, and then captured on a1. Furthermore, the other black bishop, on h2, must also have been a promoted pawn, from g1, based on white's pawns again. It could have been f, g, or h, but for simplicity I'd guess the f-pawn. It must have captured something on g2 then moved to g1. If you count that up, that's 6 white pieces that must have been captured by those two pawns. As white still has 10 pieces, that's all of them accounted for. This means that the piece on g4 must be black.

However, with black to move, this position, for the moment, seems impossible. What was white's last move? it couldn't have been any of the pawns, because then a black piece couldn't be where it is. It couldn't have been the king, because the only place it could have come from is b1, but it would have been in check there, and we've already established that the only place the a2 bishop could have come from is b1. The bishop couldn't have been it either, because it didn't have anywhere to come from. This leaves the rook, but the only square from it to come from is e1, where it would have been checking the black king, making black's previous move illegal.

Solve the mystery above, and I'm sure you'll solve the puzzle.

However, to the OP, your question of whether black can castle suggests its own answer. You could not, in such an advanced game state PROVE that black can castle, but you might be able to prove that he or she cannot. So the answer is no, though I haven't proven it yet.

Is the board flipped so black can't castle?

50 or so :)

Anyways, Winder, you are on the right track, but there is a fallacious assumption in the second paragraph.

Just remember, these positions for these puzzles are often improbable to arrive at, but not impossible.

I'm not sure all of that is true, WanderingWinder. Could blacks black-squared bishop not have gone to h2 before white played g3?

Following WanderingWinder's reasoning, the problem with the second paragraph is that there's a third option for the move that White just made that does not have the problems that the other two listed do:  O-O-O.  This must have been White's last move

This means that the Black piece on g4 can't have been a Bishop or a Queen otherwise White wouldn't have been able to castle.  So the options are now:  A Black Knight, a Black Pawn or a Black Rook.

The only way the black white-square bishop could be in that position is if it is on h7?

so g4 would be... the white queen? and of course black couldn't castle

White's last move was O-O-O.

Looking a little more closely:

The pawn that ended up being the Bishop on a2 had to capture at least five pieces on its way to promotion -- four to get to the a file assuming it started on e7 (the conservative assumption) and one more to promote on the white square.  This is clear from the position of White's Queen-side Pawns.

I don't see the necessity for the other Black Bishop to have been a promoted Pawn, however.  It could easily have arrived at it's current square before the White Pawn was moved to g3.

So with five white peices confirmed captured, but six missing do we know for certain that it is not a White peice on g4?  I don't know that we do.

Without knowing for certain that it's not a White peice on g4, we can't make any deductions about White's last move as I did in my last post, nor can we say for certain whether Black can or can't castle....

Hmmm....

Here is my guess. The piece on g4 is a white pawn, and it just captured a black piece from f3. As to whether black can castle, the result is inconclusive. The bishop on h2 does not have to be a promoted pawn.

I don't think a guess will suffice -- I suspect that when you see the answer and the reasoning behind it it will be clear that it is the correct solution.

White's last move can't have been O-O-O because the bishop on a2 would prevent it.

no Cerdog - a castling can be prevented only if the king's path is crossed by opponent piece - it does not matter if the rook's path is crossed.

The bishop on h2 can get there through natural means. g4 has a light squared bishop on it.  Otherwise, it would not be tricky.

dsarkar - Really? I always thought it was if any square from the king to the rook (inclusive) was under attack. You learn something every day, I guess.

No it wouldn't -- the Rook can pass through a line of attack as long as the King doesn't.