Looking for the Killer

Logic Level 2

In our extraordinary game,

  • Black has castled in the last move,
  • In one of the 3 previous moves, the white knight from g1 was captured on its initial square.

Which piece captured the knight?

This problem is the second of the set Retrograde Chess .
b8 Knight h8 Rook King f7 Pawn a8 Rook g8 Knight Queen f8 Bishop

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Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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1 solution

  • Note that Black hasn't moved the Pawn on g7 and the Pawn on e7, so the Bishop from f8 was captured on his initial square, because the Bishop couldn't go out. Hence, the Bishop is not the killer.
  • Now, look at the Pawns on b7, c7, d7 and e7; they also haven't been moved. Thus, the Bishop from c7 hasn't been moved from his initial square. As the black has just castled, it means that the King wasn't moved before last move, therefore, the Queen was enclosed and was captured on her initial square... maybe by that Knight on d8. Briefly, the Queen is not the killer.
  • Since the Bishop hasn't been moved, and looking at the position of the a and b Pawns, the Rook from a8 couldn't go out to kill the Knight. That is, the Rook from a8 is not the killer.
  • As the black has just castled, the Rook from h8 and the King haven't been moved. Consequently, neither the h8 Rook nor the King are the killers.
  • Note that the Knight that now is on a5 could not capture the White Knight, because the piece was captured in one of the 3 previous moves. So, the Black Knight could not capture the white Knight and then scape to a5. Although that a5 Knight seems suspect, he is not the killer.
  • Consider the Pawn on e2. As he hasn't been moved, the g3 Black Knight couldn't come from e2. If he captured the White Knight, then, in one of the 3 previous moves, he was on g1. But to go from g1 to g3, he needs at least 4 moves, and the Knight was captured in one of the 3 previous moves. Hence, the g3 Knight is not the killer.
  • Therefore, the killer is the Pawn from f7. His long journey was like this: He captured the White Bishop from c1 on h2, g3, f2 or g5. He also captured the h1 Rook on h2, g3, f2 or g5. Necessarily, one of them was captured on h2 or f2. Then, he captured the Knight on g1 and was promoted. Finally, he was captured, possibly by the King.

As Sherlock said, "when you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth."

26 Helpful 3 Interesting 5 Brilliant 4 Confused

That's how I solved this problem. Nice!

Seth-Riley Adams - 5 years, 1 month ago

I solved the same way!

Rohan Gupta - 4 years, 11 months ago

Nice problem ! I answered the queen, and then I realized that the queen is captured by the knight. (since the queen has no way out )

Gema Baskara - 4 years, 10 months ago

Nice problem! However, can you construct a game showing that this position is indeed possible?

William Nathanael Supriadi - 4 years, 6 months ago

@Mateo Matijasevick , how do you know that it wasn't the h7 pawn which captured it (and not just because it isn't one of the answer options). Surely the pawn on h4 could've originally been the f7 pawn?

Very interesting problem though.

Stephen Mellor - 3 years ago

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Count the white missing pieces: g1 knight, both bishops, a pawn and a rook. For the h7 pawn to capture the g1 knight, it must have captured previously on g3 and then either on f2 or h2, which are black squares, so, summarizing, h7 pawn must have captured 3 pieces on black squares. Therefore, the f7 must have captured the other 2 pieces in order to get to the h column, and one of these pieces must have been the f1 bishop, as it runs on white squares... but this bishop couldn't get out, thus the setting is impossible

Mateo Matijasevick - 3 years ago

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