White mates in 3

Originally posted by THUDandBLUNDER
White to play and mate in 2 moves.

[fen]4k2r/p1p1p1p1/1p2P3/8/3R4/6P1/5P1P/R3K3[/fen]

Hmmm......Clearly the only way white can mate in two is Rad1.....Rd8++. However this only succeeds if it can be proven that black is unable to castle.

We can see that blacks f-file bishop is off the board and given that the e and g pawns have not been moved it would follow that it had to be captured. But by what? This is pivital and the missing black h file pawn now becomes significant.

Obviously the capture was not with the white bishop as there is no path and it cannot have been the Knight as this would not have forced the recapture. Since both white rooks are still in play the conclusion is that the Queen captured the bishop with check forcing the recapture either by the King or rook and thereby removing the option of castling. I think thats got it.

skeeter

Originally posted by Mephisto2
isn't it sufficient that there is no proof that black lost his castling right? Apart from a flaw in my set of premises (which I hope you will show us if that is the case), then I think we cannot exclude black castling and hence, escape from mate in 3.

Black can castle implies White can't castle.
White can castle implies Black can't castle.

The convention is that one side castling prevents the other from doing so.
Hence 1. O-O-O means Black can't castle.
If 1. Rad1 Black castles.

Originally posted by skeeter
Hmmm......Clearly the only way white can mate in two is Rad1.....Rd8++. However this only succeeds if it can be proven that black is unable to castle.

We can see that blacks f-file bishop is off the board and given that the e and g pawns have not been moved it would follow that it had to be captured. But by what? This is pivital and the missing black ...[text shortened]... ing or rook and thereby removing the option of castling. I think thats got it.

skeeter

I have not understood why it could not have been a white knight capturing the bishop. Why was recapture necessary? The knight may have moved away by itself (and become captured later on somewhere else)?

The whole problem is based on the fact that if one of the sides can castle the other can't, so by castling you thereby confirm that White is the side that can castle and not Black, or else the problem would have no solution 🙂

Originally posted by Mephisto2
I have not understood why it could not have been a white knight capturing the bishop. Why was recapture necessary? The knight may have moved away by itself (and become captured later on somewhere else)?

Its imperative to understand that the piece capturing the Bishop had to be a "checking" piece forcing the re-capture by the King/Rook, so to prove that they moved, so to establish that black cannot castle. The Knight capture does not provide this proof. Besides, moving the Knight away would normally have captured the pawn, unless it was a 'help mate'

skeeter

Originally posted by skeeter
Its imperative to understand that the piece capturing the Bishop had to be a "checking" piece forcing the re-capture by the King/Rook, so to prove that they moved, so to establish that black cannot castle. The Knight capture does not provide this proof. Besides, moving the Knight away would normally have captured the pawn, unless it was a 'help mate'

skeeter

It's not *IMPERATIVE*. The only thing that is imperative is that Black is not able to castle: leading to the only possible conclusion that the Rook at d4 was promoted. But it was obviously promoted on the 8 rank, so how did it get to d4? Considering the possible routes it is obvious that it was either through h8, f8, or d8 all of which imply that Black king or Rook must have been moved.

Originally posted by THUDandBLUNDER
Black can castle implies White can't castle.
White can castle implies Black can't castle.

The convention is that one side castling prevents the other from doing so.
Hence 1. O-O-O means Black can't castle.
If 1. Rad1 Black castles.

I am lost now. Can you post the full and correct solution to either problem?

Originally posted by Mephisto2
Where is this convention documented? I have never seen that before (which is quite possible since I am not a specialist in this, but awaiting that I remain unsatisfied)). It certainly looks a strange convention to me, as it is a deviation from normal chess rules.

Mephisto you are missing the point:
If White can castle in the first problem then the bishop is not promoted so the last move cannot be 1..g6 and therefore Black cannot castle.
That is 1.O-O-O means Black cannot castle.
The same in the second problem. Since to be able to castle White must have promoted the rook at d4 then Black must have moved either their King or their Rook disabling the option of castling, hence again 1.O-O-O means Black cannot castle.
The point is that it is either White or Black that can castle but not both, so by castling White states Black's castling as illegal.

Originally posted by ilywrin
Mephisto you are missing the point:
If White can castle in the first problem then the bishop is not promoted so the last move cannot be 1..g6 and therefore Black cannot castle.
That is 1.O-O-O means Black cannot castle.
The same in the second problem. Since to be able to castle White must have promoted the rook at d4 then Black must have moved either the ...[text shortened]... Black that can castle but not both, so by castling White states Black's castling as illegal.

I still feel uneasy with positions that are defined only by the NEXT move to be made. If white plays 1.Rd1 then black can castle, and if white plays 1.0-0-0, then black cannot castle. I understand what is being said, but still ....

Originally posted by ilywrin
Mephisto you are missing the point:
If White can castle in the first problem then the bishop is not promoted so the last move cannot be 1..g6 and therefore Black cannot castle.
That is 1.O-O-O means Black cannot castle.
The same in the ...[text shortened]... both, so by castling White states Black's castling as illegal.

You are missing the point. neither white nor black can castle. After reaching that the rest is logical.

skeeter

amazing puzzles both

and skeeter: how can you be sure that neither can castle?

Originally posted by Jusuh
amazing puzzles both

and skeeter: how can you be sure that neither can castle?

Well actually its irrelevant if white can castle or not. Given chuck'n chunders statement that white can mate in two it follows that black must be unable to castle. Otherwise the solution fails.

skeeter

Originally posted by Mephisto2
I still feel uneasy with positions that are defined only by the NEXT move to be made. If white plays 1.Rd1 then black can castle, and if white plays 1.0-0-0, then black cannot castle. I understand what is being said, but still ....

In general, it is assumed that one side can castle unless it can be proved that it cannot.
And with mutually exclusive castling the adopted convention is as I stated previously.
That is, White can castle because we cannot prove that he cannot.
Thus Black cannot also castle.

Originally posted by skeeter
Well actually its irrelevant if white can castle or not. Given chuck'n chunders statement that white [b]can mate in two it follows that black must be unable to castle. Otherwise the solution fails.

skeeter[/b]

Is this also 'imperative to understand'?

Originally posted by skeeter
Well actually its irrelevant if white can castle or not. Given chuck'n chunders statement that white [b]can mate in two it follows that black must be unable to castle. Otherwise the solution fails.

skeeter[/b]

You are correct that black must be deprived of the right to castle, but incorrect about why black cannot castle.

White could have played Nxf8 in the past. We can't prove that Black recaptured, so this won't help us prove Black can't castle.

However, white plays 1.0-0-0! and it's a different story. The rook on d4 could not come from h1, as you pointed out. The only other alternative is that it's a promoted white pawn. The promoted Rook can only escape the 8th rank via d8, f8, or h8, all of which require a move of the black King or Rook, thus proving that black has no right to castle.

So, as others have pointed out, white's 1.0-0-0! destroys black's right to castle.