Correct me if I'm wrong, but wouldn't one (or two even) of the Three make Sauron even more powerful? I do agree (even though I had not thought of it before until it was mentioned here) that he knew there was a Ring in Rivendell and another in Lorien. I don't know exactly how strong both cities were, but why didn't he attack them and recover at least two of the three? then he'd be even mightyer and he might have been able to crush Gondor in spite of Aragorn and Gandalf's best efforts.
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