The simplest question that has already been proven by Alan Turing that a computer can never be able to answer. "Is my program looping?" Sounds like a simple question, but it is in fact undecidable and known as the Halting Problem. You can know in certain obvious situations whether it is looping or not, but you can't apply a technique to all programs to determine whether it is or not. This question doesn't just apply to today's computers, but computing theory, meaning that no matter how much memory is applied, no matter how fast it is running, no matter if it is deterministic or not, if you were to create a program using the full capabilities as the computer answering the question, it can never fully know whether the program is looping or not.
Of course, by rewording your question we can come up with another, "What is a question that you are unable to answer?". If a computer is able to answer this question, then the answer to this question is a question that they are unable to answer. But if they are unable to answer this question, that means that they are unable to answer this question. Surprisingly, they can never be unable to answer this question, simply because if they were unable to answer this question, then the answer is this question, but it can't be because this question now has an answer which is itself. Therefore there always has to be an answer other than itself.