by garykevinware » 2 July 2010, 6:00 pm
Regarding the 4/1990 CL KK H#2.5:
To show what Black's last move was, we show what White's last move was, and to show that, we show what Black's penultimate move was, and to show that, we show what Black's penultimate move was not. En route we show that Black must have made a minimum of ten captures and had already made all those captures before his penultimate move by showing, among other things, how the BPs arrived at their current positions and that these positions enforce further constraints.
Since all of Black's men are currently on the board,
(1) vacuously, all of Black's Pawns are currently on the board,
(2) none of White's men had ever made a capture
So each of White's Pawns that is currently on the board either never moved (i.e., WPe2, WPg2) or moved straight up the file on which it is currently (i.e., WPc7 moved straight up the c-file, WPf5 moved straight up the f-file, WPh6 moved straight up the h-file).
To account for Black's Pawns,
(1) BPb7 has never moved
(2) BPa7 must have gone to e3 via four captures and is currently blocked from behind by BBd4
(3) since WPc7 exists, BPd7 must have gone to c6 via one capture and is currently blocked from behind by BBd7
(4) so BPc7 must have gone to d5 via one capture and is currently blocked from behind by BPc6, but Black could not have moved this Pawn from d6 on his penultimate move, since, as we see later, White would have had no legal move
(5) so, since WPf5 exists, either BPe7 must have gone to e4 via no capture and BPf7 must have gone to f3 via two captures, or BPe7 must have gone to f3 via one capture and BPf7 must have gone to e4 via one capture; in either event, BPe4 is currently blocked from behind by WPf5, and BPf3 is currently blocked from behind by BPe4, BRf4, and BPg4, and Black could not have moved his Pawn from e5 on his penultimate move, since, as we see later, White would have had no legal move
(6) so BPh7 must have gone to g4 via one capture and is currently blocked from behind by BPg5 and WKh5
(7) since WPe2 and WPg2 have never moved and nothing currently occupies f1, Black had already captured WBf1
Since White has six men currently on the board, and in light of (7), any supposed movement of Black's Pawns running contrary to (1)-(6) above would necessarily imply that Black had already made more than ten captures, an impossibility. One could establish that Black could make these ten captures legally by producing a theoretical game score, which seems evident from the above analysis and the analysis to follow. Since Black had already made all of his captures before his penultimate move, White could not have made his last move by moving an object followed by Black immediately capturing it. Hence Black had already made exactly ten captures, none of them as his last move.
Since WPc7 is currently blocked from behind by BPc6, since WPf5 is currently blocked from behind by BRf4, and since WPh6 is currently blocked from behind by WKh5, White's last move could not have been a WP move and hence must have been a WK move. WK could not have come from either g4 or h6, since WK is currently blocked by BPg4 and WPh6, neither of which could have moved immediately prior.
BSh4 could not have come g2, f3, or f5, all of which are currently occupied, and so either came from g6 (which cannot be, since White would have failed to make a legal move once) or was where it is currently. Further, h4 is also currently attacked by BPg5, buttressed by BQf6, and g6 is also currently attacked by BQf6 and BSe7. So, for a number of reasons, WK could not have come from h4 or g6.
BPg5 could not have come from g6, since WK currently occupies h5. So, for the problem position to be legal, the last move must have been BPg7->g5, and immediately before that, WKg5->h5, and immediately before that, BQ moved from somewhere (there are several squares available) to f6. This sequence locks White's objects into place, so Black's last move could not have arisen from anything other than the BP that we just showed must have two-stepped from g7 to g5.
Since BPg7->g5 must have been Black's last move, WPf5->g6 e.p. is legal, and the solution follows.
This problem appears as #619 in Key Krackers and as #418 in Edgar Holladay's posthumous publication "U.S. Chess Problem Anthology" (Vampade, 2004). (but the anthology had an error: the BPc6 that should be in the diagram isn't there.) Supposedly this problem earned a "B+" grade, which (as I understand things) is a very good grade.
Regarding the (3-4)/1990 USPB H#2.5:
To show what Black's last move was, we show what White's last move was, and to show that, we show what Black's penultimate move was, and to show that, we show what Black's penultimate move was not. En route we show that Black must have made a minimum of twelve captures and had already made all those captures before his penultimate move by showing, among other things, how the BPs arrived at their current positions and that these positions enforce further constraints.
Since all of Black's men are currently on the board,
(1) vacuously, all of Black's Pawns are currently on the board,
(2) none of White's men had ever made a capture
So each of White's Pawns that is currently on the board either never moved (i.e., WPc2) or moved straight up the file on which it is currently (i.e., WPa7 moved straight up the a-file, WPe5 moved straight up the e-file).
To account for Black's Pawns,
(1) BPf7 has never moved
(2) so BPh7 must have gone to e4 via three captures and is currently blocked from behind by BSf4
(3) so BPg7 must have gone to d4 via three captures and is currently blocked from behind by WPe5
(4) so either BPd7 must have gone to c4 via one capture and BPe7 must have gone to d5 via one capture (this combination we show impossible, later), or BPd7 must have gone to d5 via no capture and BPe7 must have gone to c4 via two captures; in either event, BPd5 is currently blocked from behind by BQe6, and BPc4 is currently blocked from behind by WKc5 and BPd5
(5) so BPc7 must have gone to b4 via one capture and is currently blocked from behind by WKc5
(6) so BPb7 must have gone to a6 via one capture and is currently blocked from behind by BBb7, and BPa7 must have gone to b6, then to a5, via two captures and is currently blocked from behind by BRb6
Since White has four men currently on the board, any supposed movement of Black's Pawns running contrary to (1)-(6) above would necessarily imply that Black had already made more than twelve captures, an impossibility. One could establish that Black could make these twelve captures by producing a theoretical game score, which seems evident from the above analysis and the analysis to follow. Since Black had already made all of his captures before his penultimate move, White could not have made his last move by moving an object followed by Black immediately capturing it. Hence Black had already made exactly twelve captures, none of them as his last move.
Since WPa7 is currently blocked from behind by BPa6, and since WPe5 is currently blocked from behind by BPe4, White's last move could not have been a WP move and hence must have been a WK move. WK could not have come from either c4 or d4, since WK is currently blocked by BPc4 and BPd4, neither of which could have moved immediately prior.
If Black's last move had been from anything other than the BP that we show later must have two-stepped from d7 to d5, then White would have failed to make a legal move once. Further, b6 is currently attacked by BBc7, and c6 is currently also attacked by BBb7 and BQe6. So, for a number of reasons, WK could not have come from b4, b5, b6, or c6. Further, d6 is also currently attacked by BBc7, BQe6, and BSf5. So WK could not have come from d6.
BPd5 could not have come from d6, since WK currently occupies c5. So, for the problem position to be legal, the last move must have been BPd7->d5, and immediately before that, WKd5->c5, and immediately before that, BQ moved from somewhere (there are several squares available) to e6. This sequence locks White's objects into place, so Black's last move could not have arisen from anything other than the BP that we just showed must have two-stepped from d7 to d5. Since BQ blocks BPd5 from behind, the above suggestion that perhaps BPd7 must have gone to c4 via one capture and BPe7 must have gone to d5 via one capture is impossible.
Since BPd7->d5 must have been Black's last move, WPe5->d6 e.p. is legal, and the solution follows.
Both problems illustrate the Valladao theme (en passant, castling and promotion all present).
