-4

As far as I can calculate, 6 is the limit for the most number of pawns on a single file possible. Is 7 possible at all, ignoring promotion? I only took into account using the edge of the board, not the center, so I may be wrong.

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If you only include legal positions then 6 is the limit. The pawns could possibly occupy the 2nd-7th ranks, via diagonal captures towards the desired file.

If you ignore promotion and allow pawns to be on the 8th rank (or 1st rank for Black's POV) then the limit is 7.

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Addendum 9/2/2020-It turns out that the shortest possible game is actually 16.5. moves long. This problem was published in The Die Schwalbe Chess Problem Database.

[Title "Henrik Juel & James Malcom, PDB Website 7/77/2020, Non-Unique Proof Game In 16.5 Moves"]
[FEN ""]

1. g4 Nc6 2. g5 f6 3. gxf6 Nd4 4. fxe7 Nf6 5. exd8 Nd5 6. a4 b5 7. axb5 c6 8. bxc6 Bd6 9. b4 Ba6 10. e4 Bd3 11. cxd3 O-O 12. cxd7 Rc8 13. exd5 Rc5 14. bxc5 Rf3 15. cxd6 Re3+ 16. fxe3 Kh8 17. exd4

Using black pawns-my thanks goes to @DM for this idea-I have completed my quest to find the shortest possible septupled pawns proof game in 18.0 moves.

[Title "James Malcom, chess.stackexchange.com 2/25/2019, Proof Game In 18.0 Moves"]
[FEN ""]

1. d4 b6 2. d5 a5 3. d6 exd6 4. Qd5 c6 5. e4 cxd5 6. b4 f5 7. Bd3 fxe4 8. c4 exd3 9. c5 bxc5 10. Be3 axb4 11. Nc3 bxc3 12. Bd4 cxd4 13. O-O-O g5 14. f4 gxf4 15. Rd2 cxd2+ 16. Kb1 f3 17. Ne2 fxe2 18. Rd1 exd1
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