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(a) 1.Rdd8 ( threatening checkmate with 2.Rh8# ) Re1+ 2.Ka2
[a1] 2. …g6 ( 2. …Ra4+?? 3.Kb3 Re3+ 4.Kxa4 g6 or Kh6 ＋－ ) 3.Rh8+ Kg7 4.Rdg8+ Kf7 5.fxg6+ Ke6 6.Re8+ Kd5 7.Rd8+ Kc5 ( 7. …Ke6?? 8.Rhe6# ) 8.Rc8+ Kb5 9.Rxc4 Kxc4 10.g7 hxg4 11.g8=Q+ Kd3 12.Qxg4 ＋－
[a2] 2. …Kh6 3.h4 g6 4.Rh8+ Kg7 5.Rdg8+ Kf7 6.fxg6+ Ke6 7.Re8+ Kd5 8.Rd8+ Kc5 ( 8. …Ke6?? 9.Rhe8# ) 9.Rc8+ Kb5 10.Rxc4 Kxc4 11.g7 hxg4 12.g8=Q+ Kd3 13.Qxg4 ＋－
(b) 1.Rdd8 g6 2.Rh8+ Kg7 3.Rdg8+ Kf7 4.fxg6+ Ke6 5.Re8+ Kd5 6.Rd8+ Kc5 ( 6. …Ke6?? 7.Rhe8# ) 7.Rc8+ Kb5 8.Rxc4 Kxc4 9.g7 Kb3 [ threatening checkmate with 10. …Re1# ] ( or 9. …Rxh3 10.g8=Q+ ＋－ ) 10.g8=Q+ ＋－
(c) 1.Rdd8 Kh6 2.h4 Re1+ 3.Ka2 g6 4.Rh8+ Kg7 5.Rdg8+ Kf7 6.fxg6+ Ke6 7.Re8+ Kd5 8.Rd8+ Kc5 ( 8. …Ke6?? 9.Rhe8# ) 9.Rc8+ Kb5 10.Rxc4 Kxc4 11.g7 hxg4 12.g8=Q+ Kd3 13.Qxg4 ＋－
1. g5 Rf4 [1…fxg5 Rdd8 +-] 2. g6+ Kh6 3. Rg1 and Black will need to give up a rook to prevent mate!
If 1.Rdd8 Kh6 and although he is much worse, it is not yet winning! 1.g5 was the played move.
Very good!