8/2p5/3P4/kr6/2p5/7K/8/3R4 w - - 0 1
a) 1...Rb8 (forced), 2. Ra1+! Kb6, 3. Rb1+ Ka7, 4. Rxb8 Kxb8, 5. d8=Q+ Kb7, 6. Qd4 and White wins
b) 1...Rh5+!, 2. Kg2! Rh8, 3. d8=Q Rxd8, 4. Rxd8 c3, 5. Rc8 Kb6, 6. Rf8! c2, 7. Rf1 Kb5, 8. Rc1 Kb4, 9. Rxc2 c5, 10. Kf3! c4, 11. Ke2 Kb3, 12. Kd2 and White wins!!!
Yes, I understand why Rf8 is the only move to win.
Illyrialady, according to my notes on this study, I pretty much settled on 1.d7 for no other reason than it was counterintuitive to 1.dxc7 which, as you note, only draws. For the me the hardest part of this puzzle was the second move and the sixth move. In some sense, I realized pretty quickly why 2.Kg2 was better than the alternatives- white must keep the king closer to c1 to stop the pawn once the rook has been won, but it took me a while to work out why 6.Rf8 was required in the second variation Alena gives above.
Alena, good. Now you can see why it had to be 6.Rf8, but not the similar looking 6.Re8, 6.Rg8, and Rh8, right?
Well, I was wrong.
According to Nalimov database, Black can draw but
only if after
- dxc7 Rc5
- Rd5 Rxd5
- c8Q Kb4!
Every other move there by Black loses.