Smullyan Problem in Sherlock Holmes book

[Christopher Heckman]

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. (Since another problem in this book was
found to have an alternate solution, the diagram was changed for the
Third Edition; the same thing might have happened here.)

The first step is to show that the White King is not on d5, e4, f3, or
g2, so Black is in check. All of these squares are under Black's
control, and since White just moved, White could not have moved into
check, and so White is not IN check.

Black's next move must do two things; it must stop this check, and
checkmate White. The only moves which can stop the check are moving
the king, Be4, Qf3, Nf3, Qg2, and Ng2.

Note that White is not in check, but that Black's move will check the
White king (for starters). So the piece Black moves will either attack
White's king, or it will uncover a piece which attacks White's king.

A king move won't work, because it doesn't open up any lines.
Similarly, Be4 doesn't attack any squares that weren't attacked
before. If the key move is Qg2, then the White king must be on g1, but
Bxg2 shows that this is not mate (contrary to assumption).

Similarly, if Qf3 is the "key move", then the White king must be on
the f-file, and Bxf3 removes the check, so Qf3 doesn't work, either.

If Black plays ... Ng2, there are two possibilities. If the knight is
attacking the king, then the king must be on f4 or h4, and Bxg2 stops
the "mate". If the knight is not attacking the king, then the rook
must be, and so the king is on g1; but Qxa1 stops that.

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 also have a few responses to problems from other books of
Smullyan's, but this is not the proper forum for them. Does anyone
know of a website which has discussions involving Smullyan's books?

Also, does anyone know anything about an retrograde analysis algorithm
which, if given a position, will deduce facts about the game?
(Something other than Euclide or Natch?)

--- Christopher Carl Heckman

[Andy Walker]

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.