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R-D4 (or R-E4) followed by R-H4 does the trick as well.
So...What if black doesn't move the king? He's not in check and does not have to. Assuming the king would move renders the puzzle kind of unclear.
No, it doesn't. g7-g5 prevents it.
nice horsea seadra moves
There are like 3 mate options...
Not to detract on this well done puzzle, but I think we'd all rather solve the puzzle of how to reach an endgame up two rooks and a knight rather than how to mate in two moves while up two rooks and a knight ...