Since it seems at least some people are enjoying these I'm continuing the series.
This one is not quite as elegant, but still interesting.
Can White Castle?
Answer
I present to you, pure inefficiency:
1. Nf3 f6 2. Nh4 Kf7 3. Nf5 Ke6 4. Nd6 Ke5
5. Nc4+ Kf4 6. Nb6 Nh6 7. Nxc8 Ng4 8. Nb6 Nc6
9. Nxa8 Nd4 10. Nb6 Nf3+ 11. exf3 Ne5 12. Bd3 Nc4
13. Bg6 hxg6 14. Na4 Rh5 15. Nac3 Rh6 16. Qe2 Rh3
17. Qe4+ Kg5 18. Qf5+ gxf5 19. Na3 Ne3 20. Ncb5 Kf4
21. Nd4 Nc4 22. Nab5 Ne5 23. Na3 Nd3+ 24. cxd3 Ke5
25. Nc6+ Kd5 26. Nb4+ Kd4 27. Nd5 Kc5 28. Nc3 Kb4
29. Ne4 fxe4 30. Nc2+ Kc5 31. Na3 exd3 32. Nb5 Rh4
33. Nc3 Rc4 34. Nd1 Rxc1 35. Rb1 Rc4 36. Rc1 Kb4
37. Rc2 Rh4 38. Ne3 Rh3 39. Nd1 dxc2 40. Nc3 Kc4
41. Nd1 Kd3 42. Nc3 Rg3 43. Nd5 Rg4 44. Ne3 Rg5
45. Nd1 Rg3 46. Ne3 c1=R+ 47. Nd1 Kc2 48. h3 Ra1
49. h4 Kc1 50. Nc3 Rh3 51. Ne4 Rh2 52. Nc3 Kc2+
53. Nb1 Kd3 54. h5 Kd4 55. h6 Ke5 56. h7 Ke6
57. h8=B Kf7 58. d3 Ke8 59. O-O
It can definitely be done faster, but this works.
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