Question:

Kimberly has an integer between -16 and 16 (inclusive) in her mind. You can ask her some questions, each of which must be in the form of "is your number strictly less than x?" (x can be any real number). You can decide the question you are going to ask according to the answers of previous questions. In the worst case, at least how many questions should be asked to know the exact value of the integer Kimberly has in mind?

Solution:

The question "Is your number strictly less than x?" gives only two possible answers, yes or no. Therefore, the best value for x is the mean of the biggest possible value and the smallest possible value. So,

First choice: x = 0. The worst case is when the answer is 'no' because this leave 0 to +16, 17 possible values.

Second choice: x = 8. The worst case is the same. This leaves us 8 to 16, 9 possible values.

Third choice: x = 12, 5 possible values

Fourth choice: x = 14, 3 possible values

Fifth choice: x = 15, 2 possible values (15 or 16)

Sixth choice: x = 16