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very nice complete sweep puzzle. Educational.
Indian teacher, I want to say this was from an actual masters game. There is a reason why a7 isn't taken. It opens a file for the rook and eventually can come out and take the pawn on a2. This would actually make it a little worse to take it since the rook can now come out and just equalize material.
I played against a computer both variants (taking a7 and not taking it). Black does not have a chance in either case. Not taking a7 looks safer but if you analyze what happens after that, it does not really matter. You see, after all exchanges White will have at least 3 passed pawns. That's enough for win.
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