Die Schwalbe

1 problem(s) found in 2016 milliseconds (displaying 1 problem(s)). [PROBID='P0002638'] [download as LaTeX]

1 - P0002638
Raymond Smullyan
The Chess Mysteries of Sherlock Holmes 1979
WeiƟ hat gerade rochiert. Befindet sich UWF auf dem Brett?
Yoav Ben-Zvi: The Black piece that accounts for the capture on a3 could not be [bBc8] (captured on a light square) so it was a missing bP that promoted. The bP promotion could not have occurred on h1 ([wRh1] did not move before castling) so the promotion was on g1 or f1. wPg3 came from g2, it could not capture on g3 as this would be the second capture by White on a dark square and Black's 2 missing pieces include [bBc8] which was captured on a light square. This means that the promoting pawn could not have been [bPg7] as this would require 2 captures on the way to promotion (to bypass [wPg2]) plus a third capture by bPh7xg6. Therefore the promoted bP comes from h7 and, to reach the promotion square, it must have captured on column g behind wPg3. If the piece captured on a3 was an "original" (not promoted) Black piece (could be any officer other than [bBc8]) then the piece promoted by Black is present in the diagram, replacing the piece captured on a3. Henceforth we consider the alternative: that the piece captured on a3 was the promoted piece itself. This implies that the capture by the bP on its way to promotion came before the capture on a3. If wBg5 is not promoted then, prior to wPb2xa3, the wB was locked at c1 which implies that [wRa1] had not yet escaped its home corner and that [wBc1] subsequently moved to g5 via b2 crossing c3. This means the White pawn was still standing on c2 and therefore, since the wK had not moved, that the wQ could not have escaped from d1. It follows (for the case of Black promotee being captured on a3) that the White piece captured by the Black pawn on its way to promotion could not have been [wBc1] or [wRa1] or [wQd1] as it has been shown that, in this case, all 3 were locked when this capture occurred. The White piece captured by promoting bP also could not have been a wP since, as noted above, wPg3 came from g2 and the capture occurred behind it. Since the White piece captured on column g could not have been one of the missing original pieces, [wPh2] must have promoted. On its way to promotion [wPh2] could not capture on g7 (with bP waiting on h7) for the same reason as given above for the capture on g3 (not all White captures were on dark squares). Therefore wP must wait on h2 until its way to promotion is cleared by bPh3xg2 so it can subsequently promote on h8 to replace the captured piece (known to be a knight). In conclusion: for every alternative scenario there is a promoted piece on the board.
The stipulation, which might be defined more accurately as "Must there be a promoted piece on the board?", weaves together the alternative strands of the solution.
The presentation of the problem begins on page 106 of the book (chapter "Shades of the Past") relaying the condition that the last move was -1.0-0 and that Sherlock Holme's nemesis, Professor Moriarty, solved the problem in less than 4 minutes while Holmes admits it took him more than 20 minutes. The description of the solution begins on page 155. (2018-12-29)
Mario Richter: @Yoav: Quote: "... to replace the captured piece (known to be a knight)." This is not completely correct.
Just a small thought to think about: Let's assume that Black answers White's castling by playing 1. ... 0-0! In what way does this change the RA? (2018-12-29)
Yoav Ben-Zvi: The conclusion that the piece captured on g2 was a wN is reached under the assumptions that Black's promoted piece was captured on a3 (therefore it is not present in the diagram) and that wBg5 is not promoted (implying that [wBc1] exited after the capture on a3 and before [wQd1] could be released by wPc2-c3). It has been shown that, under these assumptions, [wBc1], [wRa1] and [wQd1] could not have escaped in time to be captured on g2. The piece captured on g2 also could not be a wP ([wPg2] moves to g3) or a wB (wBg4 could not be promoted on the dark square h8) or a promoted piece (the path to promotion of [wPh2] is open only after the capture on g2) so I think the conclusion that it had to be a knight is justified, under the assumptions (although it is not needed to meet the stipulation).
The suggested addition of the condition: "Black retains the right to castle 0-0" prevents any resolution that has [wPh2] promoting on h8. It has been shown above that capture of Black's promoted piece on a3 requires the White promotion on h8 (either to a wB that replaces the one captured on c1 or to a wN that replaces the one captured on g2). This contradiction (promotion on h8 is required but not allowed) means that the piece captured on a3 could not have been Black's promoted piece so it was an original (not promoted) piece. The piece captured on a3 could not be [bBc8] (captured on a light colored square) or a bP so it is a bQ or bR or bB or bN that is replaced in the diagram by the promoted piece, proving that there must be a Black promoted piece present in the diagram position. A fine idea that improves the accuracy of the resolution. (2018-12-30)
Keywords: Promotion, Castling (wksk), Constrained problem
Genre: Retro
FEN: r2qk2r/ppp2p2/2np1np1/2b1p1B1/N5B1/P1P2NP1/P2PPP2/R4RK1
Reprints: Schach mit Sherlock Holmes 1982
Input: Gerd Wilts, 1995-06-03
Last update: A.Buchanan, 2018-02-28 more...
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Gerd Wilts (1)