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1. Nb5! Rxa7 [1…O-O 2. Rxc6 Rxa7 3. Bxa7 +-] 2. Rxc6 O-O [2…Ra8 3. Nc7+ Kf8 4. Nxa8 +- or 2…Rd7 3. Rc8+ Rd8 4. Rcxd8#] 3. Bxa7 +-
(a) 1.Nd5 Rxa7 2.Rxc6
[a1] 2. …Nxd5 3.Bxa7 e6 ( , 3. …Nb4?? 4.Rc8#, or 3. …Bxb2? 4.Rxd5 ) ＋－
[a2] 2. …Ra8 3.Nc7+ Kf8 4.Nxa8 ＋－
[a3] 2. …Rxa2 3.Nxf6+ Bxf6 4.Rc8#
[a4] 2. …Rd7 3.Nxf6+ Bxf6 4.Rc8+ Rd8 5.Rcxd8# or Rdxd8#
[a5] 2. …Kd7 3.Nb4+ Ke8 ( or 3. …Nd5 4.Rxd5+ Ke8 5.Rc8# ) 4.Rc8#
[a6] 2. …Kd8 3.Nxf6+ Rd7 4.Rxd7#
(b) 1.Nd5 Nxd5 2.Rxc6 Rxa7 3.Bxa7 e6 ( , 4. …Nb4?? 5.Rc8#, or 4. …Bxb2? 5.Rxd5 ) ＋－
(c) 1.Nd5 Qxd5 2.Rxd5 Nxd5 ( 2. …Rxa7?? 3.Rc8# ) 3.Qxa8+ Kd7 4.Qxd5+ Ke8 5.Rc8#
(d) 1.Nd5 Qxc1 2.Qxa8+ Kd7 3.Nxf6++ Ke6 ( or 3. …Kc7 4.Rxc1+ Kd6 5.Qd5# ) 4.Qa6+ Kf5 ( , 4. …Ke5 5.f4+ Kf5 6.g4#, or 4. …Qc6 5.Qxc6+ and White wins. ) 5.g4+ Ke5 6.f4#
(e) 1.Nd5 and provided that Black can castle on the king side, 1. …O-O 2.Rxc6 Rxa7 3.Bxa7 Nxd5 4.Rxd5 Bxb2 ＋－.
Definitely possible and winning, but white played 1.Nb5 in the game.
Very good!