Incorrect stipulation?

[Alexander George]

In the September 2007 Problemist Supplement, I published the following problem (possibly the most minimal parity problem?):


Is O-O legal?

If it's White to move, then one concludes that either the wK or the wR on h1 has moved, hence castling is not allowed. One of the comments (in the March 2008 issue) was this: "As a number of solvers have pointed out that castling would be legal if it is Black to play, perhaps the stipulation should have read 'White to play. Is O-O legal?'" Now, I don't see that. For if it's Black to move, then it seems to me that O-O is not a legal move, anymore than e4 is: these aren't legal moves because it's not White's turn to move. Whether it's White's move or Black's, O-O is not legal in this position. This is what I was thinking when I set my stipulation. Is that wrong?

[Siegfried Hornecker]

0-0 is legal for both sides if it is black to move and only for black if it is white to move.

That's the only correct solution to your stipulation.

[Alexander George]

0-0 is legal for both sides if it is black to move and only for black if it is white to move.

I guess I don't understand the conventions for saying when a move is legal. In the above position, with White to move, is Ba3 legal? To be sure, if the pawn on b2 weren't there, it would be legal. But the pawn is there, and so the move fails to be legal. Likewise, in the position above, if it's Black to move is it legal for White to castle? I would say No: it's not White's move. If it's Black to move, would it be legal for Black to castle? I would say No again: given the intervening pieces between Black's King and Rook, castling is not permitted.

I interpret the question "Is move X legal?" to mean: "In the actual position, can one legally make move X?". I don't interpret it to mean: "If the actual position were different [say pieces were removed, or it was the other side's turn] would move X be legal?".

[Joaquim C.]

"Is move X legal?" = "In the actual position, can one legally make move X?"

I would agree with this equivalence. However in the particular case of castling the only conceivable misundertanding I can imagine is:

"Is O-O legal? = "has white/black lost the right to O-O?"

[Michael McDowell]

Joaquim is correct. Those who solved the problem interpreted the stipulation as “Has White lost the right to O-O?". The suggestion for the rewording of the stipulation came from me as column editor. I’m no expert on retros so I don’t know if there is an accepted way of wording such stipulations; all I can say is that (rightly or wrongly) I would have interpreted the given stipulation in the same way as the solvers.

[reddmann]

Since I'm the "master of confusion", another aspect (apart from the fact that
"Is O-O legal" can be interpreted so and so): Assume it's a help problem and it's
only relevant if White *may* castle. Then Black could "steal" the right to move
and White legalize that by castling. Standard wacky AP logic.

[Siegfried Hornecker]

This isn't possible! En passant was shown by Nenad Petrovic but your idea of stealing a move is just impossible.

[jsalai49]

The stipulation implies that the white has to move, and it is correct.
The initial position is legal with white to move.

The move:
NN. O-O
is not legal!
The white Rook has moved before!

The proof:
It is a simple and straight "domino" retro-problem.
Black made his moves only with his knight(s)!
As knight changes its field color at every move. black (and white too) have made an EVEN number of moves before, so "NN" must be an ODD number!
The white - to move - had to gain (or lose) a tempo, since his knight made an ODD number of moves (being on f3 - white field - initially on black). The white King could not gain/lose a tempo ("domino" color change), so the only piece possible to break this "symmetry" is the white Rook. The shortest proof game (one of them):

1.Nf3 Nf6 2.Ng1 Ne4 3.Nf3 Ng3 4.Ng1 Nxf1 5.Nf3 Ng3 6.Rf1 Nf5 7.Rg1 Nh6 8.Rh1 Ng8

and

9. O-O is not legal

Sorry for my bad English