Solution Time for "A problem courtesy of Sergey Karjakin"

Back at the end of February, I posted a problem Sergey Karjakin had tweeted:

White to play and win

Karjakin joked that this was a simple position. The first move is easy enough, at least!

(I have written up the solution as a blog post, and put it in a replayable window below.)

ADDED: I've decided maybe a little extra explanation might be in order. White's goal of queening his f-pawn can be achieved one of two ways: White can gain a tempo to play f8(Q) with his king guarding the f8 square (forcing Black to give up his rook), or he can deflect the Black rook from the eighth rank for a move. Furthermore, the deflection cannot occur with a check, unless White can then take the Black rook safely, or no tempo would be gained. To accomplish these goals White wants to shield his king from lateral checks. He cannot do that by moving his king to the g-file, since Black's king controls the critical squares g7 & g8. So White must get his rook between the Black rook and his own king.

After 1 Ke7 Rc7+ (both forced) we have a position that occurred in a study by N. Kopaev, 1953. I found this position in Dvoretsky's Endgame Manuel, 2nd ed. as Exercise 9-1, pg 144. This is NOT the initial position of the study, which I don't have. Here's Dvoretsky's starting point:

2 ?

"The unlucky placement of the king kills Black (with the king on h7 it would have been a draw); in addition,his rook is too close to the f-pawn. But it is by no means easy for White to exploit these disadvantages." - Dvoretsky  
                                                      2. Kf6
Trying to approach the rook with the White king allows the rook to escape to a safe distance. 2. Ke8 Rc8+ 3. Kd7? Ra8!*

And 2. Ke6 merely transposes since after 2... Rc8 (2... Rc6+ 3. Kd7 Rf6 4. Ke7+-) the King can't approach and must go to f6 anyway. 3. Kf6.
                                                      2    ...     Rc6+  
                                                      3. Ke5!

The White king must step carefully and keep close to the Black rook. 3. Kf5? Rc5+! 4. Ke6 Rc8!= 5. Kd7 Ra8 Again the rook has escaped to a safe distance.
                                                      3    ...     Rc8
"If 3... Rc5+ then 4. Kd6! Rc8 5. Re1 Kg7 6. Re8+- With a rook on b8, the saving check Rb6+ exists." -Dvoretsky
                                                      4. Rg6!  
 This move wouldn't be possible if the Black king were on h7.
                                                      4    ...    Kh7
4... Rb8 5. Rb6 Ra8 6. Kf6 Kh7 7. Re6 Kh6 8. Re8 Ra6+ 9. Ke5 Ra5+ 10. Kd4 Ra4+
11. Kc5 Ra5+ 12. Kb4 Rf5

                                                      5. Rc6!  Ra8
5... Rxc6 looks like the better practical try. Dvoretsky ignores it because he assumes if you don't already know how to win Q vs R, you'll learn it in Chapter 13! I don't have table bases loaded up, but Stockfish gives this as mate in 18 from this point. I'll let the interested reader work it out for himself!                                       
                                                      6. Kf6
"The rook protects the king from side checks. Black is helpless against the maneuver Re6-e8." - Dvoretsky

As Karjakin said, a simple position!

* I've used the Nunn Convention for the analytical marks. Dvoretsky applied standard usage. I have changed those marks to the Nunn Convention in the quoted material to avoid confusion.