Chess Logic Puzzle ♙ Where (And What) Did The Pawn Capture? ♙ Retrograde Analysis ♙ Smullyan, 1979

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In this video, the goal is to figure out whether the white pawn is on f4 or f5. To do this, one must figure out where the pieces were captured and how the current pawn structure came about. If you want to see more retrograde puzzles, let me know! Be sure to subscribe for more chess content!
Thank you!
Sample proof game to get there (not the most efficient):

10 Comments

  1. Thanks for this: tiny nit – it doesn’t have to be knights that capture the locked-in bishops. If the kings shifted, a rook or queen might have done the business. But that doesn’t affect the main solution – great stuff!

  2. I figured out by the nature of the question that the pawn had to be on f5.

    If it were possible for the pawn to be on f4, the question would be ill-posed, because I can also show it can be on f5.

    If it was White's turn to move, I can do f5 Qc7 Qf3 Qd6 Qd1 Qd8 to set the board with White's turn to move and the pawn on f5.
    If it was Black's turn to move, I can do Qc7 f5 Qd6 Qf3 Qd8 Qd1 to set the board with Black's turn to move and the pawn on f5.

    So either both positions were possible or only f5 is possible. Since the question asserts only one is possible, it must be f5.

    If it were possible for the pawn to be on f4, the question would be ill-posed, because I can also show it can be on f5.

  3. Before watching the solution part my guess is: f5
    Explanation:
    Both dark square bishops can't escape their starting position due to the positions of the surrounding pawns. So both of them were captured by the opponent's knights. So they don't participate in the pawn captures. That leaves us with a knight and a light square bishop on both sides to be captured by pawns. Since the bishops can be captured only on a square they can access (in this case both be on light squares) that means that dxc6 capture was a bishop capture so cxb6 was a knight capture. So black captures are clear. As for the white captures. In a similar way we can conclude that fxg3 can't be a light squared bishop so it has to be a knight. That means white's e-pawn captured the bishop. So it should be on either f3 (followed by potential f4 move to get to the f4 square) or f5.
    BUT!!!! If it is on f3 that means black's light square bishop is already out. But he can leave initial square only AFTER the cxb6 capture (which we already concluded was white's light squared bishop). So white's bishop must be already out ==> e-pawn has already moved. SO it is impossible for the e-pawn to make that exf3 capture. Which means the pawn has move first and then made the capture on f5. Which is the position of the pawn.

  4. who said bishop captured pawn? maybe black knight captured it but white didnt recapture and later white captured the opponent bishop with their queen

  5. You mentioned you have to choose between f5 and f4, so we don't need to consider f3 at all.
    But considering other possibilities, white pawn could be on d5 and d7.

  6. Isn't the following also possible?–

    1-White's knight b1 has captured the black bishop on c8 and the black bishop on f8, and then goes to c4.

    2-Black's knight b8 captures the white bishop on c1, then captures the white pawn on e2 and sacrifices itself on g3.

    3.-f2xg3

    4. Bf1-b5-c6

    5.dxc6

    6. Nc4-b6

    7.cxb6

    And we have the same position.
    Or is it a condition that the white pawn must be on either f4 or f5?

  7. The first retrogate I could solve. There really fun. Took me about 3 min.

  8. I love all the Raymond Smullyan books! Grew up with them and have a love/hate relationship with some of the later logic puzzles in some books as they took way too much time / focus to really get to the solution. But his chess logic book was great, and really enjoyed his story telling using Sherlock / Watson. Thanks for sharing this puzzle with the world!

  9. Really interesting. I guess the craziest part is that if you showed me the wrong position with the pawn on f4, I would never suspect I'm looking at an invalid state.

  10. The title and wording had me confused thinking the question was where the white pawn got captured. A better title would maybe be "where did the white pawn capture the black bishop".

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