If you allow questions with n possible answers, then you need at least ceil(log_n(7e9)) questions, where log_n means logarithm base n. I don't know if there is

If you allow questions with n possible answers, then you need at least ceil(log_n(7e9)) questions, where log_n means logarithm base n. I don't know if there is a simple formula for the case where different questions allow different number of answers.