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could've improved alot
The other technique is easier. After your "much longer than that" line with Kd1, yes it takes a few more moves but ultimately the king has to step into opposition and you mate...that is the basic technique. I added that line to the diagram.
The technique that roooperi demonstrated is an integral part of basic K+R vs. K endgame.
It is ludicrous for one to progress from beginner without knowing that a position such as the one below is a Mate in 2.
I was trying the "Knight's move" technique from a Chess Mentor course I did not that long ago (though it may have been with the Queen, not the Rook).
This applies for the queen, not rook. It's a slow method, but very simple, almost braindead.
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