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How did Bilbo get his ring?
Gollum had lost it, and Bilbo found it. Without knowing that it was Gollum's ring on the one hand, and without Gollum even knowing he'd lost it on the other, they have their game of riddles, and the rather unfair question Gollum could not answer was, "What is it in my pocket?" To late Gollum found out that it was his ring, Bilbo put it on and ran away with it.