Inspired by a recent question posed by Roger Penrose, what is the smallest number of legal chess moves to get to this position?
Improving on Glorfindel's very clever solution, I produced the following version that takes only 37 moves (instead of 42).
1.d4 c5 2.d5 Nc6 3.dxc6 f5 4.e4 fxe4 5.f3 exf3 6.h4 fxg2 7.Nf3 g1=B 8.Bc4 d6 9.Bxg8 g5 10.Bxh7 g4 11.Bd2 g3 12.Bb4 cxb4 13.Na3 bxa3 14.Qd5 g2 15.Qc5 dxc5 16.h5 Be3 17.Rh4 g1=B 18.Rb4 cxb4 19.Bf5 Rxh5 20.Bxc8 Ra5 21.b3 Ra4 22.c4 Qa5 23.Rd1 Bg7 24.Rd6 exd6 25.Ne5 Kd8 26.Nd3 Kc7 27.Bd7 Kb6 28.Be8 Rxe8 29.Ke2 Re5 30.Kf3 Rb5 31.Nc5 dxc5 32.Ke2 Ka6 33.Kf3 b6 34.Ke2 Bf4 35.Kf3 Bgh2 36.Kf2 Bhg3+ 37.Ke2 Bge5
The key was to realize that black's move are much more precious than white's and that black's march of the h pawn (only to get rid of it) is rather inefficient when the white bishop can also do it.
Here is the .png if you want to replay it.
[FEN ""] [Event "?"] [Site "?"] [Date "????.??.??"] [Round "?"] [White "?"] [Black "?"] [Result "*"] [CurrentPosition "8/p7/kpP5/qrp1b3/rpP2b2/pP4b1/P3K3/8 w - - 8 38"] 1.d4 c5 2.d5 Nc6 3.dxc6 f5 4.e4 fxe4 5.f3 exf3 6.h4 fxg2 7.Nf3 g1=B 8.Bc4 d6 9.Bxg8 g5 10.Bxh7 g4 11.Bd2 g3 12.Bb4 cxb4 13.Na3 bxa3 14.Qd5 g2 15.Qc5 dxc5 16.h5 Be3 17.Rh4 g1=B 18.Rb4 cxb4 19.Bf5 Rxh5 20.Bxc8 Ra5 21.b3 Ra4 22.c4 Qa5 23.Rd1 Bg7 24.Rd6 exd6 25.Ne5 Kd8 26.Nd3 Kc7 27.Bd7 Kb6 28.Be8 Rxe8 29.Ke2 Re5 30.Kf3 Rb5 31.Nc5 dxc5 32.Ke2 Ka6 33.Kf3 b6 34.Ke2 Bf4 35.Kf3 Bgh2 36.Kf2 Bhg3+ 37.Ke2 Bge5 *
Proof that this is the shortest solution (incomplete step in the end, maybe crucial)
10 moves: To get the pawn structure on the left black needs 10 moves (9 moves for the black pawns, 1 move (Nf6) to get white’s pawn to f6).
4 moves: To get the black king where it belongs (Ke8 – Ka6, ideal route)
7 moves: To get black rooks and queen to finishing position (Q needs one move, Rh8 needs 3 (Rh8-h5, h5-a5, a5-a4), Ra8 needs 3 (Ra8-e8, e8-e5, e5-b5). Q & Rh8 follow ideal routes, Ra8 route cannot be improved as pawn on a7 is needed) needs one move, Rh8 needs 3 (Rh8-h5, h5-a5, a5-a4), Ra8 needs 3 (Ra8-e8, e8-e5, e5-b5). Q & Rh8 follow ideal routes, Ra8 route cannot be improved as pawn on a7 is needed)
10 moves: To promote two bishops you need 10 moves (five for each) on the ideal route.
6 moves: To get three bishops in position you need two moves per bishop. Bf8 needs to moves to get to any of the fields (e5, f4, g3) The same is true for both bishops if they are promoted on g1. Only if either of the bishops could be promoted on e1, c1 or a1, a move could be saved. Now that both bishops have to be promoted on g1 feels difficult to prove. Promotion on c1 and a1 are out of question because getting either of the f, g or h pawn that far left would cost too many white pieces. Promotion on e1, however, seems at least theoretically possible.
If last step were correct, sum would be 37 moves and hence the solution provided here the shortest possible.
If there is any room to get 36 rather than 37 it is by promoting one of the bishops on e1. Please, try your luck.
UPDATE: Seeing as how the OP asked for a GIF of this in the comments, a GIF has been made using Apronus, using what the editor believes is a reasonable frame rate.
Here is a solution where the position is reached in 42 moves:
1. d4 c5 2. d5 Nc6 3. dxc6 f5 4. e4 fxe4 5. f3 exf3 6. h4 fxg2 7. Nf3 g1=B 8. Bd2 d6 9. Bb4 cxb4 10. Na3 bxa3 11. Qd5 g5 12. Qc5 dxc5 13. Rd1 g4 14. h5 g3 15. Rh4 g2 16. Rb4 cxb4 17. Rd6 exd6 18. h6 Nxh6 19. b3 Nf5 20. Bd3 h5 21. Bxf5 h4 22. Bxc8 h3 23. Bxh3 Rh5 24. Ke2 Ra5 25. c4 Ra4 26. Ne5 Qa5 27. Nd3 Kd8 28. Bf5 Kc7 29. Bg6 Kb6 30. Be8 Be3 31. Kf3 Rxe8 32. Ke2 Re5 33. Kf3 Rb5 34. Nc5 dxc5 35. Ke2 Ka6 36. Kf3 b6 37. Ke2 g1=B 38. Kf3 Bf4 39. Ke2 Bgh2 40. Kf3 B8d6 41. Kf2 Bhg3+ 42. Ke2 Bde5
The game can be replayed here.
Certainly not an optimal solution
Here is a way to get to that position, as a baseline for others' improvements. I bet it can be reduced quite a lot:
1. b3 d6 2. Ba3 Nc6 3. Bc5 dxc5 4. Qc1 g5 5. Qa3 h5 6. Qb4 cxb4 7. Na3 bxa3 8. d4 Rh6 9. g4 hxg4 10. Nf3 g3 11. Ne5 g2 12. Nc4 g1=B 13. Nd6+ exd6 14. Rd1 g4 15. Rd3 g3 16. Rc3 g2 17. Rc5 dxc5 18. h4 Nf6 19. Rh3 Bh2 20. Rc3 g1=B 21. Rc4 Bh3 22. Rb4 cxb4 23. Bxh3 Rh5 24. f4 Ra5 25. d5 Ra4 26. e3 Ne5 27. fxe5 c5 28. e6 fxe6 29. Bxe6 Nd7 30. h5 Ne5 31. h6 Bxh6 32. c4 Rc8 33. Ke2 Rc6 34. e4 Qa5 35. Bf5 Kd8 36. Be6 Kc7 37. Bf5 Kb6 38. Be6 Ka6 39. Bd7 Rb6 40. Bc6 Rb5 41. Bd7 b6 42. Bc6 Nxc6 43. dxc6 Bf2 44. e5 Bxe5 45. Kd3 Bhf4 46. Ke2 B2g3
The game can be replayed here.
Obvious but overlookable constraints to bear in mind:
- The black pawns on a3 and b4 have to get there from d7 and e7 (or some broadly equivalent combination -- you can shuffle things around a bit), capturing at least 6 white pieces on the way.
- The white pawn on c6 has to get there from the d-file or something further right, making at least one capture.
- Two black bishops have to be promoted, obviously on dark squares, implying at least one further capture of a white piece to make way plus one more either to make way (if the pawns promote on different files) or to get the black pawns onto the same file (if they promote on the same file).
- A little caution is needed to get the black pieces into place in the right order. E.g., if the black pawn on c5 is getting there from c7 in the obvious way then it had better do so before there's a white pawn on c6; once those two pawns are in place it's too late to get the black rooks inside the structure on the left; etc.