chess - Can you stop the rambling rook?

This is a chess puzzle someone showed me a long time ago. If you already know this puzzle please give the others a chance to solve it first. This puzzle was originally created by Otto Gallischek and it was published in Weser-Kurier on 1960-02-25. The problem can be seen here on the website Yet Another Chess Problem Database. It is also featured in this Chess Base article.

There is one small change though-this puzzle has a White queen instead of a rook on h3, as the original problem has.

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Above you see a position where white is obviously on the winning side. The queen is one step from giving a checkmate. And the heroic h pawn made his way from h2 to c7 and is waiting for a promotion. However, black saw a last chance and moved Rf3+ in the last turn. The rook can't be taken, because black couldn't move anymore which is a stalemate (= draw). If the king moves away the rook will continue to give checks.

Can you stop the rambling rook and find a way for white to win the game anyway?

PS: Computers are not allowed, and no cheating.

Answer

If white can ever stay out of check for one turn, then it can promote its pawn and put black in checkmate. So in order to play perfectly, black must attempt to put white in check with every move. In turn, white should make sure that black has only one option for a check in the next move, or else the rook will "break free" and have much more influence over white's moves.

White's overall game plan is to sacrifice pawns and maneuver the king until black falls into a simultaneous capture+checkmate.

 1. e3          Pawn moves forward to block rook.
 1. ...   Rxe3+ Rook captures pawn and places king in check.
 2. c3          Pawn moves forward to block rook.

 2. ...   Rxc3+ Rook captures pawn and places king in check.
 3. Ka2         King begins a "serpentine" maneuver, which will continue until move 9.
 3. ...   Ra3+  Rook takes only available move to put king in check, continuing until move 9.
 4. Kb1   Ra1+ 
 5. Kc2   Rc1+ 
 6. Kd3   Rc3+ 
 7. Ke2   Re3+ 
 8. Kf1   Re1+ 
 9. Kg2   Rg1+ 
10. Kf3   Rxg3+ Rook captures pawn in row 3 and places king in check.

11. Ke2         King begins serpentining back to column A.
11. ...   Re3+  Rook continues to pursue.
12. Kd1   Re1+ 
13. Kc2   Rc1+ 
14. Kb3   Rc3+ 
15. Ka2   Ra3+ 
16. Qxa3#       Queen takes rook and places black king in checkmate.