Hardest Mate in 4 of All Time

What you say is completely right, but what about the second possibility? Black has either captured a promoted piece or one of the white rooks.

First point means black cannot castle and second white cannot. How are the rules in chess composition when you can only prove that one side cannot castle, but can't prove which?

The convention used in compositions is the Codex of Chess Compositions, in this case Article 16.3:

"Partial Retrograde Analysis (PRA) convention. Where the rights to castle
and/or to capture en-passant are mutually dependent, the solution consists of
several mutually exclusive parts. All possible combinations of move rights,
taking into account the castling convention and the en-passant convention, form
these mutually dependent parts. If in the case of mutual dependency of castling
rights a solution is not possible according to the PRA convention, then the
Retro-Strategy (RS) convention should be applied: whichever castling is executed
first is deemed to be permissible." (emphasis mine)

In this case, we apply PRA first. The castling rights in FEN notation "Kk" is provably impossible, "K" gives us mate in 2, and "k" gives only mate in 5. Therefore we have to apply RS: Whoever castles first denies the other the right. Whence the solution, where white scrambles to castle first.

This position lies in the realm of chess problems, not regular chess games. Thus we have the apply the problemists' rules - the Codex. (Which I might add, is also used by FIDE for their FIDE album composition awards, if you insist on some appeal to authority.)

It is not in standard chess rules and not even in standard chess composition rules, but it is in the retrograde conventions. The diagram counts as an RS (retro strategy) problem which operates on the 'first come, first served' principle. In casu, first castling is legitimate, the second one is disallowed.

I didn't know that rule thanks for clarification!

https://www.chess.com/blog/Harish73/the-hardest-puzzle-ever-seen

So as a part of the mating solution White must castle to disprove that Black can castle? So you can't mate in two moves by promoting the pawn?

@nicholas

Yes, but you have to prove that Black can't castle.

And if you take for granted that Black can't castle why didn't you directly play b7 and then mate? Why move the knight?

Amazing problem. I had never heard of such a rule.

It looks like there was someone who got it right :D

However, I will clear up the confusion tomorrow, in approximately 24 hours :)

Castling One other special rule is called castling. This move allows you to do two important things all in one move: get your king to safety (hopefully), and get your rook out of the corner and into the game. On a player’s turn he may move his king two squares over to one side and then move the rook from that side’s corner to right next to the king on the opposite side) However, in order to castle, the following conditions must be met:

1)it must be that king’s very first move

2)it must be that rook’s very first move

3)there cannot be any pieces between the king and rook to move

4)the king may not be in check or pass through check

Notice that when you castle one direction the king is closer to the side of the board. That is called castling kingside. Castling to the other side, through where the queen sat, is called castling queenside. Regardless of which side, the king always moves only two squares when castling.(https://www.chess.com/learn-how-to-play-chess)

So if I'm correct and black includes all of these rules, black can castled whenever he wants until one/many of them aren't include (sorry for mistakes).

@Another-Life: Yes, you're getting it. In the given position, it can't be that both sides can castle, but it could be that either only white can castle, or only black can castle. Thus, "first-comes-first-served" by RS, and whoever castles first in the play forward from the diagram can legally do so, and then the other side can't.

So white can't mate in 2 by promoting the pawn, because 1. b7? 0-0, which is legal by the convention.

And exactly right: If white castles at some point in the solution, that is legal by RS (first-comes-first-served) and since white/black castling is mutually exclusive (proven by caveatcanis), black can't castle after white does. Hence, after 1. Qc4 bxc4 2. 0-0, black no longer has the defence ...0-0 and mate in two more moves follows.

@lordulords: The rules are indeed as such. But I can say the same of white. So white can also castle whenever he wants. And the thing is, if white castles, it means that in the diagram position he already (or rather, still) had castling rights. Using this fact and the piece and pawn positions in the diagram, I can then deduce with certainty that black had previously moved the king or rook in getting to this position (from the usual chess game starting position, by a legal - if nonsensical - game.) So once white castles, black can no longer castle! (This is basically a less formal way to explain PRA/RS.)

When a directmate problem is presented whose solution depends on the retrograde conventions, is it normal to identify it as an RS problem, or is the solver expected to figure that out?

Depends on if the OP wants to avoid confusion or is a drama queen.

Not necessarily. It could be that the way the problem was stated is perfectly acceptible under the rules for judging compositions. I just don't know if that's the case, and was hoping for an answer from someone who does know.

@eveningstarandlion: I'm not sure what you're asking. 1. Qc4 bxc4 2. 0-0 (legal by PRA/RS) is the main line, which implies that black must have previously moved king or rook. Put another way, it is impossible to find any game leading up to the diagram position in which all four of the wKe1, wRh1, bKe8 and bRh8 had never moved.

@n9531l: The way the problem is stated here is perfectly acceptable, yes. (Minus the fact that the FEN this site demands comes with extra information: castling rights/move number/e.p. validity etc. Ideally only the board position FEN is given.) It is sufficient to present the board and the stipulation "Mate in 4".

Due to the way the Codex lays out the rules, it is in fact necessary to assume that every directmate problem might have a retro component. The PRA/RS conventions (a more detailed analysis given here) apply to all problems - see here examples of confusion when castling conventions (the simple ones, not PRA/RS) they slip into a mainstream publication. Of course, it's up to the solver to deduce whether it's a simple PRA problem, an RS problem, or perhaps neither. To specify in the stipulation which it is is to defeat the point of the problem.

That makes sense, but makes the solver's task more complicated than I had realized it might be.

solver must know castling rights of both colors before trying to solve problem.

if,

1. black can't castle - its M2 , 1.b7 ... 2.b8Q#

2. black can castle - no mate in 4 moves!

its absurd to know which one of 1 & 2 is true after Qc4 bxc4 O-O.

@kiloNewton: You have a fine intuition for absurdity, but that is how the convention is intended indeed.

There is a way to retrain your intuition but it requires the full understanding of RS-logic which is not provided anywhere in or near the Codex. In fact, the whole retrograde community is in a continuous state of mystery about its own logics which explains why it produces insane conventions. This will be corrected in time.

Three of the keys to the mystery:

A. A diagram is not a position. In a position all rights must be known, a diagram corresponds to a cluster of positions with different rights and generated by essentially different proof games. Which position you are playing, depends on the variation you choose.

B. Some moves in an RS-solution do not eliminate black defenses directly but eliminate proof games that would allow black to set up those defenses - like castling. In the problem at hand, 1.Qc4  prevents castling directly, while 2.0-0 prevents it by eliminating proof games where black had castling rights.

C. There must always be a proof-game for every variation played, but there need not be a proof game for all variations collectively.

In the CODEX for Chess Composition Rulebook, you always-always assume castling is okay....unless you're told otherwise.

http://www.saunalahti.fi/~stniekat/pccc/codex.htm

See....Part One / Chapter IV / Article 16 / (1).