Chess Logic Puzzle ♚ Is Castling Legal? ♚ Retrograde Puzzles

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In this video, the goal is to prove that black CANNOT castle. To do this, one must show that the King or the Rook must have already moved. If you want to see more retrograde puzzles, let me know! Be sure to subscribe for more chess content!
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Here is the PGN to reach the position in a game:
1. Nc3 Nc6 2. Na4 Ne5 3. Nb6 Nf3+ 4. gxf3 g5 5. Nxc8 g4 6. Nb6 g3 7. Bh3 Bg7 8.
Nc4 Nf6 9. Bf5 Nd5 10. Bd3 Nf6 11. Nh3 g2 12. Rf1 g1=R 13. a4 Rg3 14. hxg3 Bh6
15. b4 Be3 16. fxe3 Rg8 17. a5 Rg5 18. b5 h5 19. c3 h4 20. g4 Rh5 21. g5 Rh6 22.
g6 Rh5 23. g7 Nh7 24. g8=R+ Nf8 25. Rg2 Rh6 26. Bc2 Rh7 27. d3 Rh8
28. Ra4 Rh7 29. Ba3 Rg7 30. Bb4 Rg6 31. Bb3 Rg8 32. a6 Rg7 33. b6 Rg8 34. Na3
Rg7 35. c4 Rg8 36. c5 Rg7 37. c6 Rg8 38. Ra5 Rg7 39. Bc4 Rg8 40. Bb5 Rg7 41. Rg4
Rg8 42. Bc5 Rg7 43. Rga4 Rg8 44. Bb4 Rg7 45. Qb3 Rg8 46. Kd2 Rg7 47. Ra1 Rg8 48.
Ra2 Rg7 49. Kc2 Rg8 50. Kb2 Rg7 51. Ka1 Rg8 52. Nf4 h3 53. Nd5 h2 54. e4 h1=N
55. Ne3 Ng3 56. d4 Rg6 57. Nec2 Rg5 58. Ne3 Rc5 59. dxc5 Nf5 60. Nec4
Ne3 61. Nd2 Nd5 62. exd5 Ng6 63. d6 Nf4 64. e4 Nd5 65. exd5 Kf8 66. Ndc4 Kg7 67.
Kb2 Qh8 68. Kc2 Kf8 69. Kb1 Ke8 70. Kc2 Qe5 71. f4 Kf8 72. fxe5 Ke8 73. Kb1 Kf8
74. e6 Ke8 75. Ka1