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The Toughest R+P Ending I Know

Can you find white's winning plan without consulting the tablebase? This the toughest R+P vs R ending I have seen.

8/k7/8/8/8/7P/2r5/1R5K w – – 0 1

The idea is actually quite simple. But it is difficult for amateurs to understand the move sequence. This is a very good exercise to learn R & P endgame.

I had to work out a few variation to understand why they don't work before I could find the first move. I considered Rg1, h4 and Rb5. After that I could understand the main idea of this puzzle.

1.Rb4! Ka6
2.h4 Rc1+
3.Kg2 Rc8
4.Kh2 Ka5
5.Rb3 Ka4
6.Rh3 Kb5
7.h5 Rh8
8.h6 Kc5
9.Kg3 Kd6
10.Kf4 Ke7
11.Kg5 Rg8+
12.Kh5 Rh8
13.Rc3 Ke6
14.Rc7 Ra8
15.h7 Kf6
16.Kh6 Rd8
17.Rb7 Ra8
18.Rb3 Kf5
19.Rf3+ Ke4
20.Rf7 Ke5
21.Kg7 Ke6
22.Rf8 Ra7+
23.Kg6 Ra2
24.h8=Q Rg2+
25.Kh7 Rh2+
26.Kg8 Rxh8+
27.Kxh8 Kd5
It's a winning position for white.

Consiser 1.Rb3 side by side with 1.Rb4. Then you can explain why 1.Rb4 works. I don't want go through the entire line you give, Alena, but I think black can force white into a Q vs R ending with best play.