Recently, I have been dabbling in composing a few retrograde chess puzzles. This one, I feel, turned out quite nice:
In the game leading to the position below, White somehow lost both their rooks and knights. For each of them, can you determine where they were taken and by which piece?
(Bonus points if you are also able to find a shortest possible proof game.) Please provide your reasoning in your answer.
Reasoning:
1/ e8 must be a promoted pawn.
2/ 6 black pieces are available for pawn captures on white squares; all are needed to promote the a-pawn, including Black's g-pawn.
3/ Black's g-pawn must promote to be captured by White's a-pawn; it must capture a knight at f2 and another piece.
4/ The last move must be a capture fxe8, or black would have no previous move.
5/ Only a knight could have moved there and must have captured something that did not attack the king, i.e. a knight.
6/ The black king must have moved into final position after the white king and queen, i.e. from f7. This means the black f-pawn is not captured at f7.
Due to the required g-pawn promotion, only 1 capture is available to the f-pawn. Since it must be captured by White's a-pawn, its only move must be fxe6.
So the knight captures are: gxf2 and Nxe8.
And two other captures by pawns (i.e. the rook captures) are fxe6 and fxg1.
Minimum:
31 White moves are required (see picture, captured white pieces that needed to move are shown with green circles, the knight requires 8 moves since it needs to capture black's a-rook).
This minimum is possible:
1. Nc3 Nc6 2. Nd5 Nd4 3. Nb6 Nb3 4. Nxa8 Nxc1 5. f3 Nb3 6. axb3 g5 7. Ra6 g4 8. Re6 fxe6 9. Kf2 Kf7 10. Kg3 Kf6 11. Kh4 g3 12. Nh3 Bh6 13. Nf2 gxf2 14. Rg1 fxg1=Q 15. Kh5 Kf5 16. Qe1 Nf6+ 17. Kxh6 Qg8 18. Qg3 Qg4 19. Nb6 Qc4 20. Qg8 Qgc5 21. Qd8 Rf8 22. Kg7 Ng8 23. Kh8 Kg6 24. Nd5 Rf4 25. Nf6 Q5d5 26. Ne8 Kf7 27. bxc4 Kf8 28. cxd5 Rf7 29. dxe6 Nf6 30. exf7 Nxe8 31. fxe8=B
A (not the shortest) proof game:
1. Na3 Nc6 2. Nc4 Na5 3. Nb6 Nb3 4. Nxa8 Nxc1 5. f3 Nb3 6. axb3 g5 7. Ra6 g4 8. Re6 fxe6 9. Kf2 Bh6 10. Kg3 Nf6 11. Kh4 Rf8 12. Qe1 Nd5 13. Kh5 Rf4 14. Qh4 g3 15. Nb6 Kf7 16. Nc4 Qh8 17. Nh3 Qd4 18. Nf2 gxf2 19. Rg1 fxg1=Q 20. Kxh6 Qc5 21. Qh5+ Kf6 22. Qe8 Kf5 23. Kg7 Nf6 24. Qd8 Qd5 25. Nd6+ Kg5 26. Ne8 Rc4 27. Kh8 Kg6 28. Ng7 Kf7 29. Ne8 Qe3 30. Ng7 Qeg5 31. Ne8 Qg6 32. bxc4 Kf8 33. cxd5 Qh5 34. dxe6 Qf7 35. exf7 Nxe8 36. fxe8=B
So the white rooks and knights are being captured on
g1, e6, f2 and e8
Constraints:
Obviously, the white Be8 must be
the a file pawn after capturing in each of its six moves, all on white squares. As black is only missing 8 pieces of which the black squared bishop and the Queen's side rook can be ruled out, all other missing black pieces must have been lost to that pawn including a promoted g file pawn. As such promotion is only possible via f2-g1 or f2-e1 and the white queen is still alive whereas the black squared bishop never left its starting position this ties a knight to f2.
Now let us ponder the final few moves.
It must be black's turn because the only possible black move would have been Kf7-f8 and then how did the bishop get to e8? So white must have moved last and it must have been a capture and promotion on e8.
Prior to that both kings must somehow get in which implies that the black f file pawn must have been out of the way before the white pawn came in. As the black f pawn still has to be eaten by the white pawn it must have captured on e6 and must have captured a rook because we will see in a moment that the only remaining knight must have been captured on e8. Indeed, once the white pawn arrives at f7 there are no legal moves of the surviving black pieces.
So a non surviving piece must have made back's last move and it must then have been captured on e8. But e8 cannot have been empty because the black king would have been in a check that could not have been the result of a legal white move. We have there fore tied the second knight to e8. And the rooks must now have been captured on g1 and e6.
Apologies for the messy explanation.
