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1.f7 and black has no satisfactory response.
Well, the first move has to be either f7 (to guard g8), or Kb8 just to evade mate on the next move, but f7 is obviously the better move:1. f7Now, black cannot take the pawn with the knight since the recapture followed by Kb8 allows one of the two white pawns on the seventh rank to queen. Also, putting the rook behind the f-pawn on the first move also loses to Kb8. The only really plausible move for black is...1. .....Rc12. f8Q Rc83. Qc8 Nc8Now, it is tempting to try to win with Kb8 here, but if white plays 4.Kb8, black takes at a7 and has Nc6+ in reserve if white pushes the e-pawn. It will do white no good to try a variation of this line:4. Kb8? Na75. Kc7 Nb5!6. Kd7 Kb7!And the knight will guard e8 from c7 with the support of his king.So, at move 4, white really has only two options to win- b3 or b4. The latter move is the one you want:4. b4!Threatens b5+ if black takes at a7. Black is in zugzwang. If he plays Kb5, white plays Kb8 to win the knight who has to take a7. If he plays b5, it takes the b5 square from black's knight in a critical variation:4. .....b55. Kb8 Na76. Kc7 and now the black knight can't check from b5 as in the line I discussed earlier- the e-pawn can't be stopped now.At move 4, all black can do is move the knight to either d6 or e7, but neither works:4. .....Ne75. Kb8 Nc66. Kc7 and the e-pawn queens.
1. f7!White instantly looks better.It's unclear how black will now prevent 2. Kb8 and 3. a8=Q+E.g.1. ... Rc1 (looks critical)2. f8=Q Rc8+3. Qxc8 Nxc84. Kb8 Nxa75. e7Or1. ... Rg72. Kb8!Of course not f8=Q? Rxa7+ and draw by repetition.When white avoids this trap, black resigns.For white, there is probably something wrong with:1. Kb8(?) Rg8+2. Kc7 Nf7Strong looking knight sack.3. exf7 (e7 Re8) Rf8.I don't see how white advances here.
1. f7!...Nxf72. exf7..Rf13. Kb8!..Rxf74. a8=Q+.Kb55. Q45+..Kany6. Qxf7 winning easilyOther moves transpose into the above main variation.If 1....Rf12. Kb8!.Nxf73. exf7.Rxf74. a8=Q+..etcHarry
1)F7-Rc12)F8Q-Rc83)Qc8-Kc84)B4!-Ka75)e7!-Kb5And now...6)e8K!!Followed by Kc7#
1. f7!! Rc1(Black's only reasonable response)2. f8=Q Rc83. Qxc8 Nxc84. b4!! 1-0
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