The 18 queeens chess problem has already been brought up one CSE: Shortest possible game with 18 queens?
That is a game where all 16 pawns are promoted to Queens. But nobody who asked this yet: What about the other pieces? Why not get all 20 of every other type of piece?
Thus I went on a quest to find the fastest ways I could find it get 20 Bishops, 20 Knights and 20 Rooks.
To give credit where credit is due, I give @Laska credit on his answer to this question of mine: What is the maximum number of passed pawns in a position?
I used his 20 moves game for my Knights game and a modified one of his 21-mover for my Bishops game. I devised the opening for the Rooks game myself.
I bring you here my games so we can figure out what are the fastest ways to each one. That is my question.
If you can find an already known composition, do it! If you want to have fun and compose it yourself, look I did, do so! We shall hunt down these mysteries until we find the best or optimal answer!
[Title "20 Bishops-104 Half-Moves"] [FEN ""] 1. g4 h5 2. g5 Rh6 3. gxh6 g5 4. h4 g4 5. b4 e5 6. f4 e4 7. Nf3 exf3 8. e4 f5 9. e5 Qg5 10. Nc3 a5 11. Ne4 fxe4 12. c4 a4 13.Qb3 axb3 14. a4 b5 15. a5 d5 16. c5 Ra6 17. hxg5 Rd6 18. cxd6 c5 19. Ra4 c4 20. d4 Na6 21. Be3 Nc5 22. dxc5 bxa4 23. g6 g3 24. h7 h4 25. g7 h3 26. b5 g2 27. Kf2 Kf7 28. f5 c3 29. f6 Kg6 30. Kg3 gxh1=B 31. a6 a3 32. a7 a2 33. b6 b2 34. b7 c2 35. c6 d4 36. c7 f2 37. Ba6 f1=B 38. Bf2 e3 39. a8=B Bhg2 40. b8=B h2 41. hxg8=B d3 42. Bb3 d2 43. g8=B Bh6 44. f7 e2 45. d7 a1=B 46. f8=B b1=B 47. d8=B Be6 48. c8=B Bf7 49. e6 c1=B 50. e7 d1=B 51. e8=B e1=B 52. Ba2 h1=B
[Title "20 Knights-104 Half-Moves"] [FEN ""] 1. d4 c5 2. f4 e5 3. f5 d5 4. Bf4 Be6 5. fxe6 exf4 6. e4 f5 7. e5 c4 8. Bd3 Bc5 9. dxc5 cxd3 10. c4 a5 11. b4 a4 12. Qb3 axb3 13. a4 b5 14. a5 h5 15. g4 Rh6 16. g5 d4 17. gxh6 g5 18. h4 g4 19. Ra4 Qg5 20. hxg5 bxa4 21. Kf2 d2 22. e7 f3 23. g6 d3 24. g7 Kf7 25. Ke3 Kg6 26. Kd4 f4 27. e6 h4 28. h7 b2 29. a6 a3 30. b5 a2 31. b6 f2 32. c6 f3 33. c7 g3 34. a7 g2 35. b7 h3 36. c5 h2 37. c6 Kf5 38. Nh3 Na6 39. Na3 Nh6 40. bxa8=N gxh1=N 41. c8=N d1=N 42. e8=N f1=N 43. g8=N b1=N 44. h8=N a1=N 45. c7 d2 46. e7 f2 47. Nef6 Nb2 48. Ncb6 Nfg3 49. c8=N f1=N 50. e8=N d1=N 51. Nac7 Nhf2 52. a8=N h1=N
[Title "20 Rooks-104 Half-Moves"] [FEN ""] 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 Rb7 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.
I am fairly sure that the knight game is optimal-20 moves has been proven to be the fatest way to 16 passed pawns; the knights one each side’s first rank only move once; the kings only move 3 times each-the minimum to get out if checking range, and they are never checked after moving there.
But, as always, I could be wrong!
Just a tip: If you want to shorten the rook and bishop games, I would look into finding faster 16 passed pawns games that keep that needed pieces intact.
UPDATE: Just to clarify, in regards to that close vote, I am asking if anyone can find a faster way to get to either 20 Rooks, 20 Bishops, if 20 Knights, faster then what I came up with. You can choose to do one or all of them.
Btw, I have recently just found a way to shave off 3 half-moves off of my rook game, thus making all of my games an equivalent 104 half-moves. (I found how to do the opening one step faster, and it saved a half-move later down the line.