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An interesting endgame position

dragon60
| 3
Here's an interesting endgame that resulted from the SWFCC April Swiss G/60 tournament.   It's White's turn to play.
How can he win here?


White's plan is to exploit the slow but steady trickle of pawns along the a-file towards promotion, while holding off the Black pawn avalanche with his Knight-King duo.    Black can either go after the Knight with his King, or he can pull back and try to catch up with the a-file pawns and take them down, hoping to force White's h-file pawn to be exchanged ... and get a draw that way.   

If he goes after the Knight and pushes his advanced e-file pawn straight away, he loses outright to 1.a4 Kd4  2.a5 Kxc3   3.a6 e3  
4.a7 e2   5.a8=Q e1=Q   6.Qa5+ !!! (wins the Queen & game over)"

But what if Black pulls back with the idea of eliminating the a-file passers, play might continue as follows....