I assumed the system has rewritable memory to remember previous questions, and the lookup is (all previous questions) -> next answer. With such setup (require

I assumed the system has rewritable memory to remember previous questions, and the lookup is (all previous questions) -> next answer. With such setup (require infinite memory) the system is Turing-complete of course. If it works as you described it can't even answer "what was my n-th last question".