From: arromdee@jyusenkyou.cs.jhu.edu (Ken Arromdee)
Subject: Re: NEW retrograde analysis chess problem
Followup-To: rec.games.chess,rec.puzzles
Organization: Johns Hopkins University CS Dept.
Date: Sun, 13 Sep 1992 01:53:55 GMT

In article <1992Sep11.171612.24695@cs.sfu.ca> jamie@cs.sfu.ca (Jamie Andrews) writes:
>+---+---+---+---+---+---+---+---+
>| r | n |   |   | k |   |   | r |
>+---+---+---+---+---+---+---+---+
>| p |   | p |   | p |   |   |   |
>+---+---+---+---+---+---+---+---+
>|   |   | p |   | p |   |   | p |
>+---+---+---+---+---+---+---+---+
>|   |   |   |   |   | P |   | p |
>+---+---+---+---+---+---+---+---+
>|   |   |   |   |   |   | P |   |
>+---+---+---+---+---+---+---+---+
>| P | P |   |   |   |   | P |   |
>+---+---+---+---+---+---+---+---+
>| P |   |   | P |   | P |   |   |
>+---+---+---+---+---+---+---+---+
>| R | N |   |   | K |   | N |   |
>+---+---+---+---+---+---+---+---+

OK.  Since I goofed with a wrong answer, I may as well do a correct one.

Note what was captured.  Black captured a Q, R, and two B's.  Since his pawns
made 3 or 5 captures, they must have made 3.

White captured a P, Q, N, and two B's.  The P was captured on f5.  The N
cannot move in a monochromatic game, so was captured on g8.  This leaves the
Q and the two B's; by checking colors of squares, Black's QB was captured on
b3 and the Q and KB were captured on a3 and g3 in some order.

Consider trying to create this position from the standard chess starting
position.  Black's only possible pawn moves before capturing are f7f5 and
h7h5.  Black then must make a capture or else move his king or rook.  White
can just barely get a piece in the right place to be captured; this piece must
be his Q, KB, or R.

Since h7h5 happened early on in the game, and since White's R could have been
freed only by the g3 capture, White's R was permanently confined to h1 and h3.
We now know Black captured this R with something other than a pawn, so his 3
captures with pawns were of White's Q and B's.  The QB was captured on h6
and the Q and KB on c6 and e6.  It took the a3 capture to let out White's
QB.  The a3 capture was of Black's Q or KB, but the KB was unavailable since
the h6 capture had not yet freed it, Black lost his Q on a3.  It took the
e6 capture to free Black's Q to get there.

Only White's Q, KB, and R could capture Black's N.  We already know the R is
impossible.  After the e6 capture, Black's N is hemmed in so that White
cannot get there without putting him in check and making him move his king,
so Black's N must have been taken before the e6 capture.  This means the
first capture in the game was on c6.  The first 3 moves of the game end with
White with his KP on e4, and having lost his Q or KB; Black has his QNP on c6,
and pawns moved to f5 and h5.

Black's only freed piece is his QB, and he has no pawn moves except captures.
White's only freed piece is his Q or KB (whichever survives; assume the Q from
now on), and his only pawn move (except captures) is g2g4, which does not free
anything.  Only captures will free pieces.

There is no way for the next capture to be on Black's side, since the only
available White piece is the Q, which has to take out the Black N before it
can be killed off.  So White must make the next capture, of Black's QB on b3
or N on g8.  We need the QB to take White's R, so the capture must be White's
Q taking the N on g8.  This doesn't free any pieces; the capture after that
cannot be on White's side, so it must be Black taking the White Q on e6.
This frees one piece, the Black Q; the next capture must be of it on a3 or g3.

Getting it there takes 2 moves, so white needs 2 moves to make while waiting.
These moves are e4xf5 and g2g4 (and he better not have done them earlier).
Then White captures the Black Q.

Assume this happens on a3.  Then, White has one free piece, his QB, and can
free another only with the g2 capture.  The g2 capture necessitates freeing
Black's KB, which cannot be done in time.  So it must have happened on g3.
White must eventually capture on a3; but this requires freeing Black's KB, and
White has no way to do it.

This means that the position cannot be reached by Black capturing on his third
move, so he must move his king or rook; therefore, he cannot castle.
--
"the bogosity in a field equals the bogosity imported from related areas, plus
the bogosity generated internally, minus the bogosity expelled or otherwise
disposed of."  -- K. Eric Drexler

Ken Arromdee (UUCP: ....!jhunix!arromdee; BITNET: arromdee@jhuvm;
     INTERNET: arromdee@jyusenkyou.cs.jhu.edu)