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1. Ra7+ Kf8
2. Kg6 Ke8
3. Ra8+ Kd7
4. a7 Kc7
5. Rh8!
and after the exchanges on ‘a7’, white should be able to queen his ‘g’ pawn.
Having the pawn on a6 rather than a7 makes all the difference in the world. The most direct win is to push the black king back immediately:
1. Ra7 Kf8
Here, Kh8 loses instantly to 2.Kg6 with an unstoppable mate coming on the back rank. Playing the king to g8 isn’t very different than Kf8, but I will cover it below. Continuing:
2. Kf6
This strange looking move- allowing a possible check from f1- is probably the shorter route since it gains white a tempo. Continuing:
2. …..Rf1
Here black will still lose with Ke8 since white will just push the g-pawn: [2. …Ke8 3.g5 Kd8 (or 3. …Rf1 4.Kg7+-) 4.g6 Kc8 5.g7 Rf1 6.Ke5 Re1 7.Kf4 Rf1 8.Ke3 Re1 9.Kf2 Rg1 10.g8Q Rg8 11.Ra8+-]. Also, he will lose with 2. …Kg8: [2. …Kg8 3.g5 Rf1 4.Kg6 Kf8 (or 4. …Rf8 5.Rg7 Kh8 6.Rb7 Rg8 7.Kh6 Re8 8.g6 Kg8 9.a7 with Rb8 coming 5.Rb7 Rc1 6.a7 Rc6 7.Kh7 Ra6 8.Rb8+ will win black’s rook]. Continuing from move 2 above:
3. Kg6 Rc1 (for lateral checks)
4. Rf7 Kg8 (Ke8 5.a7 Ra1 6.g5)
5. a7 Ra1
6. Rb7 Ra6
7. Kh5 Ra5
8. g5 and Rb8+ is coming to queen the a-pawn.
Back at the very first move black could have kept his king on the g-file, but it won’t help since white can force the black king away from the g-pawn with mate threats:
1. Ra7 Kg8
2. Kg6 Kf8
3. Ra8 Ke7
4. a7 Ra6
5. Kg7 Ra5
6. Rf8! Rg5 (Ra7 7.Rf7+-)
7. Kh6+-.
White wins.
Ra7+ wins.. the idea is to move the white king down to 6th rank and move the rook alone 7th rank and slowly pushes the a pawn down.
The pawn at a6 is a win. pawn at a7 is a draw as the rook cannot move along the 7th rank