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The fastest way to get to 18 queens is known. But what are the shortest possible games with a) 20 Bishops, b) 20 Knights, and c) 20 Rooks? I have done some research of my own as shown below.

Addendum: I have removed the knight and bishop games due to faster having been found.

[Title "20 Rooks: 104 Ply"]
[FEN ""]
[startply "104"]

1. b4 d5 2. g4 e5 3. h4 f5 4. a4 c5 5. c4 d4 6. f4 e4 7. Nf3 exf3 8. Nc3 dxc3 9. d4 a5 10. e4 h5 11. b5 Na6 12. g5 Nh6 13. bxa6 b5 14. gxh6 g5 15. d5 b4 16. e5 g4 17. Bd3 Bd7 18. Be4 Bb5 19. Qd4 Qg5 20. axb5 fxe4 21. hxg5 cxd4 22. g6 h4 23. g7 h3 24. f5 g3 25. f6 g2 26. Kf2 Kf7 27. Kg3 Kg6 28. Rh2 Rh7 29. g8=R+ Rg7 30. h7 g1=R+ 31. Rg2 h2 32. f7 f2 33. e6 e3 34. e7 e2 35. exf8=R h1=R 36. Re8 f1=R 37. f8=R e1=R 38. h8=R b3 39. b6 b2 40. b7 Ra7 41. Ra2 bxc1=R 42. b8=R Rb1 43. Rab2 Rab7 44. a7 d3 45. d6 d2 46. c5 c2 47. c6 a4 48. c7 a3 49. d7 a2 50. a8=R a1=R 51. c8=R c1=R 52. d8=R d1=R
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In a Computer Chess Club archives [page], (https://www.stmintz.com/ccc/index.php?id=174242) I found, the thread author Eduard Nemeth posted four proof games, all from 1997 and by Zoltan Blazsik, for 18 queens and 20 rook, bishops, and knights.

The bishop and knight games are faster, but not the rook game.

[Title "20 Knights: 100 Ply, Zoltan Blazsik, 1997, Non-Unique Proof Game In 50.0 Moves"]
[FEN ""]
[startply "100"]

1. h4 g5 2. h5 g4 3. h6 Bg7 4. Rh3 gxh3 5. hxg7 h5 6. b4 a5 7. b5 Ra6 8. bxa6 a4 9. a7 a3 10. Bb2 axb2 11. a4 h2 12. g4 e5 13. f4 d5 14. e4 Be6 15. f5 h4 16. fxe6 f5 17. g5 h3 18. c4 Qd6 19. c5 f4 20. cxd6 c5 21. Bc4 dxc4 22. d4 c3 23. d5 c4 24. Qd4 exd4 25. a5 bxa1=N 26. a8=N c2 27. a6 c1=N 28. a7 c3 29. gxh8=N b5 30. Nb6 b4 31. a8=N b3 32. Na3 b2 33. e5 b1=N 34. g6 Na2 35. g7 Nh6 36. g8=N c2 37. d7+ Kf8 38. d8=N c1=N 39. e7+ Kg7 40. d6 h1=N 41. d7 h2 42. Nb7 d3 43. d8=N d2+ 44. Kf1 f3 45. e8=N+ Kh7 46. e6 f2 47. Kg2 d1=N 48. Nec7 f1=N 49. e7 Nhf2 50. e8=N h1=N

[Title "20 Bishops: 100 Plies, Zoltan Blazsik, 1997, Non-Unique Proof Game In 50.0 Moves"]
[FEN ""]
[startply "100"]

1. a4 b5 2. a5 c5 3. Ra3 b4 4. d4 Qb6 5. axb6 a5 6. d5 Nc6 7. dxc6 bxa3 8. b4 a4 9. b5 c4 10. Nd2 c3 11. e4 f5 12. e5 Nf6 13. exf6 f4 14. g4 h5 15. g5 Rh6 16. gxh6 g5 17. h7 g4 18. h4 g3 19. Qg4 hxg4 20. h5 g2 21. h6 gxh1=B 22. Ne2 f3 23. h8=B fxe2 24. f4 g3 25. b7 g2 26. f5 e5 27. bxa8=B cxd2+ 28. Kf2 a2 29. c4 a1=B 30. b6 d5 31. b7 d4 32. c7 g1=B+ 33. Kg3 a3 34. c5 a2 35. b8=B Ba6 36. c8=B Bb2 37. c6 a1=B 38. Bcb7 d1=B 39. c7 Bb3 40. c8=B d3 41. f7+ Kd8 42. f6 Bb4 43. f8=B d2 44. Bc5 e1=B+ 45. Bf2 d1=B 46. f7 e4 47. h7 e3 48. Bg7 e2 49. h8=B Bed2 50. f8=B e1=B

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