Proofs of Algorithm Correctness and Runtime Estimates · Guessing a Number
Lesson 11
This is how this can be achieved. Take your favorite strategy consisting of four questions where there are no wrong answers. Start asking these questions, but repeat every question two times. If two identical questions got different answers, you know for sure that one of them is wrong, meaning that your friend is not allowed to give you wrong answers anymore. Then, ask this question one more time to get the right answer. In the worst case, this way, you will ask at most \(2 \cdot 4 + 1=9\) questions.