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Most positions that could be reached, in a specified number of moves, after an en passant capture could be reached just as well without one, suggesting that such positions could not occur in unique proof games. It is, however, possible to have a pair of positions in which the unique shortest sequence of moves to get from one to the other would require an en passant capture. For example:

[Title "Goal: Black king on b6 and both pawns gone, in two moves"]
[FEN "8/1p/k/8/2P/8/8/5BK w - - 0 0"]

1. c5+ b5 2. cxb6+ Kxb6

There would be no way for White's pawn to disappear in only two moves without leaving a black pawn on the c file unless it was captured by Black's king at b6, and the only way for White's pawn to get there in two moves would be by first moving to c5 delivering check. Black's first move could not be b6, because that would leave Black in check from the bishop. If Black's first move didn't push the b pawn, however, it could not get captured on white's second move. Thus, the only possible first move for Black to reach the target position would be b5, followed by White playing cxb6, allowing Kxb6. Note that while Black would have legal first moves other than b6, none of them could yield the target position after only one additional move.

If one chooses a non-standard starting position, it's thus clearly possible for a unique sequence of moves to reach a specified other position to include an en-passant capture. Do any unique proof games that use the standard starting position have this interesting property?

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There are plenty! There are currently 158 currently in the Die Schwalbe Chess Problem Database.

For example, here is one with three consecutive en passants!

[Title "Thierry Le Gleuher, R028c Probleemblad 01/1999, 2. Preis ex aequo, Proof Game In 17.0 Moves"]
[FEN ""]

1. e4 d5 2. e5 Kd7 3. e6+ Kc6 4. exf7 e5 5. Ke2 Qf6 6. Kd3 Be7 7. f8=Q Be6 8. Qxb8 b5 9. Qxa8+ Kb6 10. Qe8 c5 11. Qg6 hxg6 12. Kc3 e4+ 13. d4 exd3+ 14. Kb3 d4+ 15. c4 dxc3+ 16. Ka3 c4+ 17. b4 cxb3#
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    Amazing. And a Ceriani-Frolkin white queen, too!
    – Rosie F
    Nov 3, 2022 at 19:34

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