White to mate in 2 (A.

This problem is a classic ! I find it much fun, not too complex, and
quite pedagogical. There is a (small) trick so that it is always a
delight to show this problem to your friends at the chess club (or
wherever). Try it !

The solution is easy: after 1. Rad1!?, B can't prevent 2. Rd8 mate.
Can't he ? B can avoid being mated with 1 .. O-O.

Is this a valid defense?  A rule (a convention) in chess problems is
that any side may castle provided it is not possible to prove (through
a retro-analysis) he has lost the right to castle.

Let's see. At first sight, nothing tells us that B may not castle
anymore. Same thing for W. But look at WRd4. If it is the original WKR,
then W can't castle anymore because the Ke1 had to let this R out or
the SE corner.  Similarly, if it the original WQR, W can't castle
anymore.  Now if it is a promoted R (why not ?) then B can't castle
anymore because the BK (or the BKR) had to move and let this promoted WR
out of the 8th rank.

So that we conclude that B and W can't both still be allowed to castle,
but there is no way to tell which one did loose his castling rights.  In
this specific case of "Mutually exclusive castlings", the general
convention is that whoever castles first is allowed, therefore
forbidding castling by the other side !!

This gives us the intended solution:

        1. Rad1 ? O-O ! and no mate

        1. O-O-O ! ... 2. Rd8#  ( 1... O-O now forbidden)

Nice trick ! Highly illustrative of the Mutual Exclusion rule.

Now a question: do you know richer examples of this Mutual Exclusion
scheme ? E.g. a problem with all four castlings, involved in some
threat or some defense, but with some mutual dependencies.

-- Philippe Schnoebelen <Philippe.Schnoebelen@imag.fr>

In <3ifouq$4nd@gap.cco.caltech.edu> whuang@cco.caltech.edu (Wei-Hwa
Huang) writes:

>In other words, the winning move is O-O-O because if that were not
>a legal move, then White would have no mate in two.  Is that allowed?
>In that case, I think the question should have been "Given that White
>can mate in 2, what is the mate?"  I don't think the original
>stipulation of "White to mate in 2" is sufficient.

Yes it is. Someone can castle in a composition UNLESS it can be proven
that he (or she?) can't castle. for instance : in the given position
white may castle. If white had 8 pawns on the board, white couldn't
castle, because the rook on d4 would have been an impossibility. Hope
this makes things clear. Btw another problem which includes castling:

--------
--------
-k-P----
--------
--------
--------
-r------
R---K---

White wins (forgot the name of the composer :( )

-- Joost de Heer <joostdh@sci.kun.nl>

[ Editor: no solution to the second problem was found in the collected
postings. ]