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Yeah! You got it! Once you figure out the first move, no matter what black replies, you can mate in 2 moves either way! Most puzzles is like this, often there are few acceptable moves for black to reply and for each one white can mate with this or that piece, but I always have to choose only one response for black, and I always try to post the most coherent ones. I could post the other solutions as you did, but I think it's not necessary. I think it's better for people to figure out the others possibles solutions by themselves if black responds different way, as did yourself! ;-)
The first move you have to think a bit in a mate in 2 puzzle, then the last one is normally quite obvious!
Yeah, the second move in mate in 2 is straightforward.
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