The Pawn Endings: 6th rank King ahead of Pawn always wins

In this position you can see the white king on 6th rank ahead of own pawn which is clear winning for white. White to play or black to play its win for white.

1.Ke6  Ke8 
Take some time and just calculate here. if you push the pawn whether it reaches 7th rank with or without check.
2.d6  Kd8 3.d7 reaching 7th rank without check
3… Kc7 only move
4.Ke7 next any moves Queening.

If Black to play
1… Ke8 2. Kc7 Outflank 2… Ke7 3.d6 unstoppable Queen, wins for white.

Same like previous one. White King on 6th rank ahead of its own pawn. White to play or black to play wins for white. 

White to play
Just check if you push the pawn, whether it reaches 7th rank with or without check! 
1.g6??  Kf8 2.g7+  Kg9 3.Kg6 stalemate.
1.Kg6!!  Kh8 (1… Kf8 2.Kh7  Kf7 3.g6 unstoppable Queen) 2.Kf7  Kh7 3.g6+   Kh8 4.g7+  Kh7 5.g8=Q wins for white.  

Black to play
1… Kf8
Just check if you push the pawn, whether it reaches 7th rank with or without check! 
2.g6  Kg8 3.g7  Kh7 4.Kf7+-.
*Note: Rook pawn is exceptional 

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