How many bits of information do I get with every answer when I am guessing the number? There are three possible answers: lower, equal, or higher. It must be more than 1 bit because when guessing a number from 1 to 3, one question is enough to determine the correct number, but log_2(3) = 1.58 which is 2 when rounded up to the nearest integer. I can see, that it would be exactly 1 bit of information, if only two answers would be possible (i.e. you are not allowed to use integer numbers in the question, so you must chose, for example, number 1.8 and then the answer 'higher' will not solve the problem).
This is probably a standard question in many math courses, but it has been a long time since I was visiting the school. So, I am asking this just for my curiosity because this question is really troubling my mind.