Alice and Bob play the 1-lie version of the numbers guessing game again. But this time, although Bob still has 15 questions, Alice's number is between 1 and 2000.
For those who missed the previous problems in this series, the details:
Alice thinks of a number between 1 and 2000, and Bob makes up a list of 15 questions.
Alice then receives the list, answers all of the questions with yes or no, with the guarantee that at least 14 are answered truthfully, and returns the list to Bob.
Now, Bob must guess Alice's number.
Is it possible for Bob to uniquely identify Alice's number with 15 questions?
Clarification: Bob may not ask self-referential questions (e.g. "Is your answer to this question a lie?"). No logical paradoxes, please! Questions asking about the truthfulness of answers to other questions are allowed.