Well, that helps a little, but apparently there are 5 to 35 discrete bits of information needed to arrive at a conclusion. Once the necessary bits of info have been obtained, there may be a number of ways to arrange them to arrive at the answer. The current Yes/No approach suggests that binary logic could be used to obtain the answer. The clever use of binary arithmetic may achieve the answer more quickly. However, the necessary bits of information must still be collected from the user.
I suggest collecting the first 5 bits and from them determine the possible solutions, eliminating or confirming them with the minimum number of additional inputs possible.