More complicated pawn endgames
Rule of the square
You can use the rule of the square to determine if the King can capture the opponent pawn.
You create a square whose one edge is equal to the number of squares required in order to promote.
Black to move. Black can capture the pawn because Black King can enter into the square .
Black to move. Black cannot capture the pawn because Black King cannot enter into the square.
Black King must be on the same file with the pawn. Then it should move to the file of White King.