The three of you are put in adjacent cells. In each cell is a quantity of apples. Each of you can count the number of apples in your own cell, but not in anyone else’s. You are told that each cell has at least one apple, and at most nine apples, and no two cells have the same number of apples.
The rules of the challenge are as follows: Each of you will ask Kurt a single question, which he will answer truthfully ‘Yes’ or ‘No’. Every one hears the questions and the answers. After that, he will free you only if one of you tells him the total number of apples in all the cells. Only one guess is allowed (in total, not per person).
Pip: Is the total an even number?
Blossom: Is the total a prime number?
You have five apples in your cell. What question will you ask?
For bonus points: what would have been smarter questions for Pip and Blossom to ask?