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As usual, the moves in bold are from my game against Stockfish. Other moves are suggested improvements.
1...Kg5!
1...Kf5 was played by the child 2.Rc5+ wins, but was not played. Eventually, Black was able to promote the g-pawn, forcing White's rook off the board.
2.Kg2 h4
I remembered this idea from Engqvist, but it is not the engine's top choice as it extends the distance to mate by three moves.
2...Rb4 is best.
3.Rd3 Rf5
3...Ra4
4.Rb3 Rc5
4...Rd5 is slightly more accurate.
5.Rb2
I considered but did not fully calculate 5...h3+ 6.Kg3 Rc3+ 7.Kh2 Kh4 8.Rb4 Rc2+ 9.Kh1.
6.Ra2 Kf4! 7.Rf2+ Ke3! 8.Rb2
Rd4!
I'm hoping to exchange into an easy pawn ending.
9.Rb1 Rd2+! 10.Kg1 g3! 11.Rb3+ Rd3!
Six consecutive best moves are the result of book study and practice against the computer.
12.Rb8
12...h3
My move is based on an idea in the book: threaten back-rank checkmate, but there was a faster way to accomplish this goal.
12...Kf3 13.Rf8+ Kg4 14.Rg8+ Kh3 15.Rf8 Rd1+ 16.Rf1 Rxf1+ 17.Kxf1 Kh2.
13.Re8+ Kd4! 14.Rd8+ Kc3
14...Ke4 15.Re8+ Kf5
15.Rc8+ Kd2 16.Kf1
16...Rf3+! 17.Kg1 Re3
17...h2+ 18.Kg2 Rf2+ 19.Kxg3 h1Q
18.Rd8+ Ke2! 19.Ra8 Rd3! 20.Re8+ Kf3!
The king marches toward the rook until it runs out of checks.
21.Rf8+ Kg4! 22.Rg8+ Kf5! 23.Kf1
23...Ra3
23...h2
24.Rf8+ Kg6! 25.Rb8 g2+ 26.Kf2 Ra2+! 27.Kf3
27...Kg7
27...g1Q?? 28.Rg8+ and a draw.
27...h2!
28.Rb7+ Kf8! 29.Rb8+ Ke7! 30.Rb7+ Kf6
30...Kd6
31.Rb6+ Ke5 32.Rb5+ Kd4! 33.Rb4+ Kc3! 34.Rb1
34...h2! 35.Rc1+ Kd4
35...Kd2
36.Rd1+ Ke5!
Finding shelter behind White's king
37.Re1+ Kf5! 38.Re8 h1Q!
The rest should be easy.
39.Rf8+ Ke6! 40.Re8+ Kd7! 41.Kf4 Qh4+! 42.Kf3 Rf2+
42...Kxe8
43.Ke3 Qf4+
43...Kxe8 44.Kd3 g1Q
44.Kd3 Rd2+ 45.Kc3 Qd4+ 46.Kb3 Rb2+ 47.Ka3 Qb4#
Finishing with the queen and rook roll from Pandolfini's Endgame Course (1988), and excellent endgame resource by chess coach Bruce Pandolfini for young players.
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