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My computer shows that Rxh7+ is stornget but I expected Qc2 (even though it also wins), threatning Rc8+ and Qxg6. (The latter is easier to find for an amateur club player like me, I think.)
1. Rh7+ Kxh7
2. Qxa7+ followed by mate in few moves
1.Rh7+! Kxh7 2.Qxa7+ Kh8 3.Qb8+ Kg7 4.Qg8 mate.
Kamalakanta
“Best continuation” is the key phrase. Over the board, I would find Rf7 quickly and never look back:
1. Rf7 Qf7
This or get mated starting with Rf8 followed by Qxa7+. Or, black can give up the queen at h6 by playing Qh5+ first, but it is likely still a mate. Continuing:
2. Nf7 Kg8
3. Qa7 and white will win with ease, even if there might not be a forced short mate here.
However, the best continuation is, by definition, the shortest mate available. White can accomplish this by taking at a7 with check since the the rook isn’t actually needed for more than his noble death:
1. Rh7! Kh7
2. Qa7 Kh8
3. Qb8 with Qg8# coming in another 2 to 4 moves.
1.Rf7 Qh5+ 2.Kg2…
a)2…Qxg5 3.Rf8+ Kg7 4.Qxa7+…(4….Kxf8 5.Qf7#) 4…Kxh6 Rh8#
b)2…a6 3.g4 Qxg5 4.Qe2 Qd8 5.Qe5+ Qf6 6.Qxf6#
c)2…Qxf7 3.Nxf7+ Kg8 4.Nd6 Rxb4 5.Qf2 Nc4 6.Qf7+ Kh8 7.Qf8+ Kh7 8.Qh6+ Kg8 9.Qxg6+ Kh8 10.Nf7#