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1. Rxg6 Bf6 [1…hxg6 2. Qxg6 Bf6 3. Ng5 Re8 4. Qxf7+ Kh8 5. Bxg7+ Bxg7 6. Qh5+ Bh6 7. Qxh6#] 2. Rg3 Kh8 3. Nd5 Qd8 4. Nxf6 Qxf6 [3…Nxf6 5. Bxg7+ Kg8 6. Bxf6+ Bg4 7. Rxg4#] 5. Bxg7+ Qxg7 6. Rxg7 Kxg7 +-
I don’t see a satisfactory defense for Black in this line after 3. Nd5.
(a) 1.Rxg6 hxg6 2.Qxg6 Bf6 3.Ng5 Rd8 ( 3.Ng5 threatens checkmate with 4.Qh7#, and therefore Black can’t help playing 3. …Rd8 to avoid being mated. Needless to say, if Black plays 3. …Bxg5, then 4.Qxg7#. ) 4.Qxf7+ Kh8 5.Bxg7+ Bxg7 6.Qh5+ Bh6 7.Qxh6#
(b) 1.Rxg6 Bf6 2.Ng5
[1] 2. …Rd8 3.Rxg7+ Bxg7 4.Qxh7+ Kf8 5.Qxg7+ Ke7 6.Qxf7+ Kd6 ＋－
[2] 2. …hxg6 3.Qxg6 Rd8 4.Qxf7+ Kh8 5.Bxg7+ Bxg7 6.Qh5+ Bh6 7.Qxh6#
[3] 2. …Bxg5 3.Rxg7+ Kh8 4.Qxh7#
(c) 1.Rxg6 Nf6 2.Rxg7+ Kh8 ＋－
Well done!
Very good!