Here’s a simple challenge.
With black to cooperate and move first, and white to checkmate, checkmate black in 6 plies (half-moves.) Only one illegal move may be made, and white makes only legal moves.
State what the illegal move is.
You must also prove that the move is illegal, i.e. retrograde analysis is necessary to solve this puzzle.
The Position:
Addendum 6/13/2022: For antiquity's sake, and future reference for myself, I am tossing below the shortest possible proof game to reach this position.
1. a4 g5 2. h3 g4 3. hxg4 Nh6 4. a5 Bg7 5. a6 Kf8 6. Rh5 Nc6 7. Rha5 Nf5 8. gxf5 Be5 9. f4 h5 10. fxe5 h4 11. b4 h3 12. b5 h2 13. b6 h1=Q 14. c4 Rh6 15. c5 Rd6 16. d4 Kg7 17. g4 Qd5 18. e4 Qh8 19. g5 Qh6 20. exd5 Qe6 21. g6 Kh8 22. g7+ Kh7 23. g8=R Qf6 24. Bd2 Qe6 25. Bb4 Kh6 26. Rxc8 Kh7 27. Rg8 Kh6 28. Rg2 Kh7 29. R1a4 Kh8 30. Rga2 Kh7 31. fxe6 Kg8 32. dxc6 Kg7 33. exd6 Kh7 34. d5 Kg8 35. Bb5 Kg7 36. Na3 Kg8 37. Qb3 Kf8 38. Nf3 Ke8 39. Nd2 Rd8 40. Ndc4 Rb8 41. Kd1 Rd8 42.Kc1 Rc8 43. Kb1 Ra8 44. Ka1