I am thinking of an integer n with 0 <= n <= 15.
To figure out what number I'm thinking of, you can ask me 7 yes-or-no questions -- questions that can only be answered with either "yes" or "no".
The questions must be independent of each other, their answers, and the order in which they are answered. (So you can't ask a question like, "if the answer to the previous question was "yes", then is n larger than 10, otherwise is n even?")
When you ask me your seven questions, I am allowed to LIE about at most one of the answers. What seven questions can you ask to determine n?