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A quick view and solution1.f7!.Nd7 forced Ne6 loses to g6-g7 as king is cut off while Ke6 allows f8=Q and white wins2.g6!.Ke6 forced else g7 and queens g83.f8=Q!!.Nxf8. Forced4.g7!!!.Kf7. Forced else queens at f/g85.gxf8=Q+!.Kxf8 forced6.Kc2!.Ke7.7.Kb3!.Kd68.Ka4.Kc5.9.Kxa5! And white wins by queening his b pawn. As his king is ahead of pawn and will gain the opposition!Harry
Advancing the pawns is almost every time strong.So, f7, Nd7 (forced), g6, Ke6 (forced), and now f8Q, Nxf8 (forced), g7, Kf7 (forced), gxf8, Kxf8. And white can safely eat the a pawn, hold the opposition and promote.It really isn't that hard see, cause there are few possibilities to actually win.
1.f7 Nd7 2.g6 Ke6 3.f8=Q Nxf8 4.g7 Kf7 5.gxf8=Q+ Kxf8 6.Kc2 a4(to deny white K b3 square.without this white will easily capture black P and win) 7.Kb17.Kc3 a3 8.b3 Ke7 9.b4(trying to capture black P by Kc2-b1-a2 route fails to black's Kd6-c5-b4) a2 10.Kb2 a1=Q+ 11.Kxa1 Kd6 12.Kb2 Kc6 draws.At the same time 6.Kb1 one move earlier would have been wrong because black's P at a5 gets support by black K. 7.....a3 8.b3 Ke7 9.Ka2 Kd6 10.Kxa3 Kc5 11.Ka4 Now it is win for white.
Hard to imagine the beginning isn't one of the moves of the kingside pawns, but f7 looks interesting to me almost from the start since I can already see the possibility that white might be able to force the exchange of the knight for both pawns while, at the same time, drawing the black king far enough away from the a-pawn to give white a won K+P ending. Let's first the problem with 1.g6:1. g6 Ke6 (only move I see)2. f7If 2.g7, then black plays Kf7 controlling the pawns. Black can then secure the draw with Ne4 since white doesn't have enough time to win at a4 and queen his b-pawn: [2.g7 Kf7 3.Kc2 Ne4 4.Kb3 Nf6 5.Ka4 Kg7 6.Ka5 Nd7=]. Continuing:2. ......Ke7 (another only move?)3. Kc2 Nd7 (lots of draws)4. Kb3 Ne5 (going for g6)5. Ka4 Ng66. Ka5 Kf77. b4 Ne5 (aiming for d7 again)8. b5 Nd7And the white pawn will never cross b6.So, lets look at how 1.f7 is different:1. f7 Nd7Worse is Ne6 since it takes away a key square for black's king: [1. ...Ne6 2.g6! and g7 and a new queen at f8 or g8 can't be prevented because the king can't get through e6 just yet]. Such self blocking moves is a theme seen in lots of Troitsky puzzles, I have noticed. Continuing:2. g6Again, threatening g7 and a new queen. Black must move the king to e6 to stop the pawns. However, now white can force the exchange of the pawns for the knight:2. ......Ke63. f8Q Nf84. g7! Kf7 (else the pawn Qs)5. fg8Q Kf8And this is the position I envisioned from the very start. It is clear to me without even working through it that black cannot save the a-pawn, but let's play it out:6. Kc2! Ke77. Kb3 Kd78. Ka4! Kc79. Ka5And, it won't matter what black does from here, or could have done before- the ending is lost with the pawn.
I think I need to explain my 7.... a3 move.If 8.bxa3 with R pawn and king not reaching b7 in time leads to draw.
I was wondering whether I had erred in the variation which white should not follow by playing 8.b3 instead of 8.b4 wasting a tempo.However even that does not give a win for white.1.f7 Nd7 2.g6 Ke6 3.f8=Q Nxf8 4.g7 Kf7 5.gxf8=Q+ Kxf8 6.Kc2 a4 7.Kc3 a3 8.b4 a2 9.Kb2 a1=Q+ 10.Kxa1 Ke7 11.Kb2 Kd6 12.Kc3 Kc6 13.Kc4 Kb6 and it is draw.
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