Imagine that someone has a base-3 number system which is represented by A, B, and C. A, B, and C correspond to our usual 0, 1, and 2, but you do not know which is 0, which is 1, and which is 2. Assuming you can ask questions in terms of A, B, and C (such as “what is A + B + C,”), and you receive the answer in terms of the ABC base-3 number system, what is the fewest questions needed to solve for all of the unknowns?
Edit: There is no limit to the questions asked. The questions may include addition, subtraction, multiplication, division, and the modulus operator. The only restriction is that it is in terms of A, B, and C. Thanks again.