1. She came at all, so they all were surprised.
2. She came at any rate, so they all were surprised.
3. She came anyway, so they all were surprised.
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Does #1 mean #2 or #3? Are they all the same in meaning? Which one is commonly used?
2 and 3 mean approximately the same thing, depending on the context. 1 is not correct.
3 is probably most commonly used.