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Nxg6 wins easily
1.Nxg6+ Qxg6Alternatives make short work of black.(a)1..... hxg6 2.Rh3+ Qh7 3.Rxh7+ Kxh7 4.Qxg6+ Kh8 5.Qh7#(b)1.... Kg7 2.Nxf8+ Kh8 3.Ng6+ Kg7 4.Ne7+ Kh8 5.Qxg8#In these lines .... Qxg6 any time may transpose to main line. 2.Rxf8+ Kg7 3.Bxg6 hxg6 4.h4 White has got Q for 2 minor pieces from given position but for R and B in reality.the passed pawns are source of worry.4.... Kxf84.... a2 5.Ra8 Rb1+ 6.Kh2 a1=Q 7.Rxa1 Rxa1 8.Qxe6 is weak for black as another P is likely to fall soon.5.Qf3+ Ke7 6.Qxa3 Rc2 7.Qg3 Be8 8.Qg5+ Kd7 9.h5 gxh5 white's h5 is for clearing the diagonal h7-b1 in order to fork K and r in some cases.If 9.... g4 10.h6 can be winning line.10.Qg7+ Kd8 11.Qg8 Rc3 Here black K can not support P as 11.... Qd7 or ....Qe7 is met by 12.Qh7+ winning R.however Rc1+ 12.Kh2 Kd7 13.Qg7+ Kc8 14.Qh6 attacking R wins e pawn.12.Qxe6 d4 13.Qd6+ Kc8 14.e6 Bb5 15.Qb6 Be8 16.e7 Rc1+ 17.Kh2 Ba4 18.Qd8+ Kb7 19.e8=Q Bxe8 20.Qxe8 Still lot of play is left but I can not visualize all possibilities. My lines look to me like more of speculation rather than analysis.
This puzzle is vaguely familiar to me, but isn't in my notes, but one move is pretty obvious to me right at the start, though things are a bit more complicated than I first thought after black takes at g6 with the queen:1. Ng6! Qg6!(alternatives later)2. Rf8! Kg73. Bg6!And now, black can't take the rook:3. ......Kf8?4. Qf3I think white wins with Qf4 followed by Qf7+, too, but I like the line where white takes at a3 on move 5 better since it is just less complicated- I keep thinking I am overlooking something in 4.Qf4, and it is bothering me. Continuing:4. ......Ke7 (mate otherwise)5. Qa3Attacks the rook, too, plus it is threatening Qxc5+ winning the bishop. With b1 and c2 still covered by white's hanging bishop, all I can think of here is to play the rook to either b4 or e2/d2:5. ......Rb4Or [5. ...Re2 6.Qc5 Kd8 7.Qb6 Kc8 8.h3 hg6 9.Qb5+-]. Continuing:6. Qa7! Bd7 (Kd8 7.Qb6+-)7. Qc5 wins easily.So, let's return to black's third move in the following line, and take the bishop instead:1. Ng6 Qg62. Rf8 Kg73. Bg6 hg6!This move only looks bad- one can easily overlook that the rook can't be saved since white has to deal with the weak back rank now that the bishop has gone to heaven. Continuing:4. h4I think this is the best way. It advances the pawn further than the simple h3 and also takes away the g5 square from the black king in one of the variations I found below. White surely has the upper hand right now, but the question is, is it enough? White is going to win the a-pawn since black must take the rook either now or after playing Rb1+ first. Continuing:4. ......Kf85. Qf3!I think white must eliminate the a-pawn now. If he takes at g6/e6, black pushes a2 and I can't see any way white can win and will be forced to try for a draw by repetition. With the a-pawn gone, white will be in a position to go for a win:5. ......Kg7Hard to say where the king should go here. I guess I don't like any of the options so I am opting to protect the g-pawn with the king. Continuing:6. Qa3 Rb1I don't like Rc2 here: [6. ...Rc2?! 7.Qa7! Kf8 (or 7. ...Kh6 8.Qb8! with the double threat of Qxb5 and Qh8#) 8.Qh7 Rb2 9.Qg6 and this should be decisive]. Continuing:7. Kh2 Be8 (c4? 8.Qe7!+-)8. Qc5 Bf79. Qe7Advancing the pawns (and the white king!) on the black king right now might well be equivalent- black can't advance the d-pawn without losing it since black can't use the rook to protect it from in front, and can't maneuver the rook to d5 to do so from behind. I think white's edge is decisive now. However, I would have to think a bit longer to decide on how best to proceed from here.Finally, at move 1, black is going to get mated if he doesn't take with the queen at g6 (why Ng6 caught my eye immediately):1. Ng6 Kg72. Nf8 Kh8 (Kh6 3.Rh3#)3. Qg8! Kg84. Ne6! and there is no defense stopping Rf8#.And...1. Ng6 hg62. Rh3 Qh7 (Kg7 3.Qg6#)3. Rh7 Kh74. Qg6 with mate on the next move.
1. Nxg6+!A) 1. ......hxg6 2. Rh3+, Kg7 3. Qxg6#B) 1. ......Qxg6 2. Rxf8+, Qg8 3. Qxg8#C) 1. ..... Kg7 2. Nxf8+, Kh8 3. Ng6+, Kg7 4. Ne7+, Kh8 5. Qxg8#D) 2. Nxf8+, Kh6 3. Rh3#
1. N:g6+ Q:g61...hg 2. Rh3+ followed by 3. Q:g6+ wins.2. R:f8+ Kg73. B:g6 hg4. h4 K:f8 and White is winning.
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