12. did you lie on 1, 2, 3, 5, 7, 8, 9, 10, 11?
13. did you lie on 2, 4, 5, 6, 7, 8, 10?
14. did you lie on 1, 2, 3, 4, 6, 7, 9, 10, 11?
15. did you lie on 1, 3, 4, 5, 6, 8, 9, 11?
these combinations would ensure that even if there's a lie on any of the last four questions, the liar is caught in a trap, and from there able to determine what the binary number is. i hope that's right anyway lol