Three-digit numbers

Logic Level 1

Alice and Bob were separately told consecutive three-digit numbers. Then they had the following conversation:

Alice says, "I don't know Bob's number."
Bob says, "I still don't know Alice's number."
Alice says, "I still don't know Bob's number."
Bob says, "Now I know Alice's number!"

If they told the truth, what is the sum of Alice and Bob's numbers?

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