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With white having all pawns promoted to queens, and all pieces in their original positions, and black only having their king left, checkmated?

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Sure.

[fen ""]  
1. b4 a5 2. bxa5 h5 3. g4 b5 4. a4 c5 5. axb5 d5 6. d4 e6 7. dxc5 f5 8. e4 g6 9. exf5 Nd7 10. a6 Rb8 11. a7 Rb7 12. a8=Q Ne7 13. fxg6 Ne5 14. g7 Rh6 15. g8=Q Bd7 16. Qg5 Nf5 17. Qgd2 Nd4 18. g5 Nf5 19. g6 Nd4 20. g7 Nf5 21. g8=Q Ng3 22. hxg3 Ra7 23. b6 Ra3 24. b7 Rb3 25. b8=Q Rc3 26. Qa2 Rf3 27. Qbb2 Rff6 28. Qgg4 Rf7 29. Qge2 Rf5 30. c6 Rf7 31. c7 Rf5 32. c8=Q Rff6 33. Qca6 Rf5 34. c3 Rff6 35. c4 Rf5 36. c5 Rff6 37. c6 Rf5 38. c7 Rff6 39. c8=Q Rf5 40. Qcc2 Rff6 41. g4 Rf5 42. g5 Rf4 43. gxh6 Rf5 44. h7 Rg5 45. h8=Q Rg6 46. Qhxh5 Nf7 47. f4 Ng5 48. fxg5 Bc6 49. Qf2 Qe7 50. Qad3 Qf7 51. Qhh2 Rg8 52. g6 Bh6 53. g7 Rh8 54. gxh8=Q+ Qf8 55. Q8xh6 Bb5 56. Qdxd5 Bd3 57. Q5xd3 e5 58. Qhg5 e4 59. Qgg2 e3 60. Qdc4 Qf3 61. Qfxf3 e2 62. Qff2 Ke7 63. Q4d3 Ke8 64. Q3xe2#
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  • Here, not all pawns go back to their original position, but it now seems plausible to me that that is possible too
    – 2080
    Commented Aug 24 at 18:44
  • I wasn't paying attention to that, but no reason why they couldn't.
    – D M
    Commented Aug 24 at 18:54
  • @DM: That is merely a speed question to find the shortest nonunique proof game. Possibly Natch, Jacobi or the like could do that. OP - since the bK can safely move between e7 and e8, swapping to Q w/o check in the final position is fairly trivial. Commented Aug 25 at 7:55

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