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White really has only two plausible moves here- the rook check from h6 and the capture of the knight at h3. However, I don't think white can delay taking the knight. If white checks from h6 first, the black king can come to either g5 or e5, and after the capture at h3, black can check from b3 and exchange the rooks at h3 and get a clear winning K+P vs K ending:1. Rh6?? Ke5 (Kg5 wins too)2. Rh3 Rb33. Kg2 Rh34. Kh3 Kf45. Kg2 Ke36. Kf1If Kg1, then Ke2 and the pawn is unstoppable anyway. Continuing:6. .....f47. Ke1 f38. Kf1 f29. Kg2 Ke2 and black wins.Now, the K+P vs K ending that results from the analogous line where white captures immediately at h3 is also winning for black:1. Rh3 Rb32. Kg2?? Rh3!3. Kh3 Ke5! (Kg5 only draws now)4. Kg3 Ke4!5. Kf2 Kf4!6. Kg2 Ke37. Kf1 f4 and we saw the rest of this above.However, if, at move 2 in the line above, white plays Kf4 instead, then black cannot capture at h3 without stalemating white:1. Rh3 Rb32. Kf4! Rh3 stalemateSo, the question is this- can black win the resulting R ending with a pawn advantage? Even though I know from the puzzle's premise that the ending must be drawn, I would be 99% certain anyway- white's king is dead in front of the pawn and his rook is otherwise unconstrained- would almost surely be drawn.
1... Rxh32. Rb3 Kf4!
Spoiler alert!!!Rxh3 and if Rb3+ then Kf4
1....Rxh32.Rb6 Kf4and if black takes the rook, stalemate.
Rxh3 Rb3+Kf4!! =
Following the maxim to look at all the captures first, this comes readily to mind:1. Rxh3 Rb3+ 2. Kf4 Rxh3 stalemate
1. ... Rxh3 2. Rb3+ Kf4! (3. Rxh3 Stalemete) ½-½
1. Rxh3! Ra3 2. Kf4!! Rxh3 stalemate ( 2... Rf4+ 3. Kf3 Kg5 4. Kf2 Ra2+ 5. Kf1 Kg4 6. Rb3 f47. Rc3 f3 8. Rc8! Kg3 9. Rg8+! = with many more checks to follow or until the pawn gets undefendable by the black king. )Marcelo
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