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In timed game any player would choose 1... Rh5+ 2. Kg2 Rh2+ 3. Kf1 Kg3 and win
that was easy! FIrst try
You got white and black notations mixed up there, but this line actually makes sense, because it doesn't seem there's a way out for black after 3. Kg3, although black will make it take longer via 3... Rd2, followed by Nxd2 etc...
Tricky. But then again I suck.
Why wouldn't you just capture the rook after it was ignorant enough to put itself in your rooks path?
citizenoftheworld91 answers your question on page 10, and maybe others as well. After a disasterous RxR by white it is stalemate! White places his rook one file down (4th file) so that black cannot put its rook on the same file, because that square is defended by the white knight.
Ain't more pragmatic 4. Rg1 ?
Illegal because white is in check.