On 18/01/13 07:10, Christopher Heckman wrote:
> I was re-reading Raymond Smullyan's _The Chess Mysteries of Sherlock
> Holmes_, and I came to the section "Some Chilling Reminiscences",
> specifically the second problem. The board is given as:
>
> 8/p1p1p1p1/p1kP2p1/8/P1N3N1/1P1bP1PP/1Q1Pq2P/r3n2B
>
> (in FEN notation), with the condition that Black is to mate on the
> move; where is the White King?
>
> Smullyan provides a solution using retrograde analysis, based on where
> the White King moved from, but I came up with an alternate solution
> which does not need this. [...]
> So the mating move is ... Nf3 by elimination. If the rook is not
> checking the king, then the knight must be, and Bxf3 will stop the
> mate. If the rook is checking the king, the king must be on g1. This
> IS mate, because Black gave a double check, and no move will stop it.
> This solution requires some more case-checking, but it does not
> require retrograde analysis.
I don't have the book, but surely the point is to establish
that this position [ie, add WKg1 to the Forsyth above] is legal? If
it isn't, then the problem has no solution, So what was White's last
move? Not Pd5-d6+, which had Black in check before the move; not
Pg2-g3+ nor Pg2xh3+, for then how did White get a bishop to h1? Not
Kg2-g1+, as the K was in double-check on g2 and the N can't have
discovered check from f2. Not any Q, N or B move. So we're left
with Pc5xd5ep+ or Pe5xd5ep+, the staples of retrogression. But it
can't have been Pc5, because after retracting Pc5xd5ep+ and ...
Pd7-d5, there is again no way for White to check. So retract
Pe5xd5ep+, ... Pd7-d5, and now we can retract Pe4-45+, and there is
no problem.
Or is there? Well, yes there is, as Black has lost four
pieces, one of these the bishop on f8 which can neither have moved
nor been captured by a pawn, and white's pawns have made four
captures. Contradiction. So this line is impossible, and there is
no solution? What have we missed?
We return to Kg2-g1. A knight can't move from f2 to e1, but
a pawn can. So the checking move was Kg2-g1 in reply to ...
Pf2xXe1(N)+. What is X? Well, not the missing rooks, as Black has
captured on a6 and g6, so it must have been the missing black-squared
bishop. Replace the BNe1 by a WB, add a BPf2 and WKg2, then play 1.
... f2xB(N)+; 2. Kg1, Nf3#. Of course, now there's now no reason why
we can't also retract ... d5 and cxd5ep+. Or is there? Do we care?
--
Andy Walker,
Nottingham.