1.Ke2
Since the Black King is in the center of the board, the best way to proceed is to advance your own King.
1...Kd5 2.Ke3
As the Rook has not yet come into play, it is better to advance the King straight into the center of the board, not in front, but to one side of the other King.
2...Kc4
Should now the Black King move 2...Ke5 the Rook drives it back by 3.Rh5+
3.Rh5 Kc3
If instead 3...Kb4 there follows 4.Kd3
4.Rh4
Keeping the King confined to as few squares as possible. Now the ending may continue as follows.
4...Kc2 5.Rc4+ Kb3 6.Kd3 Kb2 7.Rb4+ Ka3 8.Kc3 Ka2
It should be noticed how often the White King has moved next to the Rook, not only to defend it, but also to reduce the mobility of the opposing King. Now White mates in three moves.
9.Ra4+ Kb1 10.Ra5
Or any square except a1 and a2 on the a-file, forcing the Black King in front of the White.
10...Kc1 11.Ra1#
In this position it took eleven moves to mate, and, under any conditions, I believe it should be done in under twenty. While it may be monotonous, it is worthwhile for the beginner to practice such things, as it will teach him the proper handling of his pieces.
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https://bit.ly/SimpleMatesTest
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