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There is an alternative and possibly better solution:
Qxd8 followed by Rc8 regardless of black's move
True. Your solution is better. Qd8 and Rc8 prevent the black queen from moving anywhere and also threaten to checkmate in the next step.
Qxd8. If the black promotes the pawn to queen. Then, the next step for white is Qxf8. The King has to kill the queen. So, Kxf8. Then, the white promotes the pawn to queen and its checkmate. d8
So, 1. Qxd8 b1, 2. Qxf8 Kxf8, 3. d8#.
1. Qxd8 Qxd8, 2. Rc8 Qxc8, 3. xc8#
1. Qxd8 Qxd8, 2. Rc8 Qf8, 3. Rxf8 Kxf8, 4. d8#
Many thanks Ashvapathi for your helpful comments!! Greatly appreciated.
3. Kg8 is a bad move, because trying to save material, black falls in the pit. If 3. Raxf8 he saves the game for a bit longer and stands a chance, but being a timed game, maybe the clock was also playing against him...
3...Kg8 is forced because 3. Nf8+ is a double check.
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