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1. Rg6
1…fxg6 2. Rxh6+ gxh6 3. Qxh6#
1…Qf8 2. Rgxg6+ gxh6 3. Rxh6+ Kg7 [3…Qxh6 4. Qxh6#] 4. Qg5#
1…Qxg6 2. Bxg6 Rf8 [2…fxg6 3. Rxh6+ gxh6 4. Qxh6#] 3. Rxh6+ Kg8 [3…gxh6 4. Qxh6+ Kg8 5. Qh7#] 4. Bh7+ Kh8 5. Qg5 Nb4 [5…gxh6 6. Qxh6 Nb4 7. Bf5+ Kg8 8. Qh7#] 6. Bf5+ Kg8 [6…gxh6 7. Qxh6+ Kg8 8. Qh7#] 7. Rh8+ Kxh8 8. Qh5+ Kg8 9. Qh7#
1. Qg5 with threat of Rg4 and then Rh4 and Rxh6+)
.. Qf8 2. Rg4
.. Qe5 2. Rxh6+ gxh6 3. Qxh6#
.. f6 2. Rxh6+ gxh6 3. Qxh6#
(a) 1.Rg6 Qxg6 2.Bxg6 Rf8 ± ( 2. …fxg6?? 3.Rxh6+ gxh6 4.Qxh6# )
(b) 1.Rg6 Rf8 2.Rhxh6+ Kg8 ( 2. …gxh6?? 3.Qxh6# ) 3.Rxd6 f6 ± ( 3. …gxh6?? 4.Qg2+ Kh8 5.Rxh6# )
(c) 1.Rg6 Qf8 2.Rgxh6+ gxh6 3.Rxh6+ Qxh6 ( 3. …Kg7 4.Qg5# ) 4.QXh6#
(d) 1.Rg6 fxg6 2.Rxh6+ gxh6 3.Qxh6#
Well done
Interesting, but 1.Rg6 wins immediately
Very good