Sextuple Rook Pawns Puzzle

Try to construct this position (from chess’s starting position) in as few moves as possible.

six_pawns

I’ve found a way to do so in 32 moves (highlight to view):

1. a4 b5 2. axb5 a5 3. Rxa5 Bb7 4. b6 Na6 5. Rh5 Nh6 6. d4 Nf5 7. Bh6 Bd5 8. b7 Nc5 9. bxa8=Q gxh6 10. Qc6 Bg7 11. Qg6 Rf8 12. e4 fxg6 13. exf5 Be5 14. dxe5 Rf6 15. c4 Re6 16. cxd5 gxh5 17. dxe6 dxe6 18. b4 Qd6 19. bxc5 exf5 20. Qg4 fxg4 21. cxd6 cxd6 22. g3 dxe5 23. Bh3 gxh3 24. f4 exf4 25. Nf3 fxg3 26. Ng5 Kf8 27. 0-0+ Kg7 28. Rf6 exf6 29. Nd2 fxg5 30. Nf3 gxh2+ 31. Kh1 Kh8 32. Nh4 gxh4

I’m pretty sure arriving at this position in fewer whole moves can’t happen, given the amount of time required for White to position pieces where necessary captures are to take place. What I think could be the case, though, is that there’s a solution that’s a half-move faster, as Black unlike White does not need this many moves (Black could castle to accelerate processes, but the limiting factor is whether the pawn captures could be expedited accordingly.

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