The best philosophical conundrums seem to have simple yes or no answers at first, but upon further inspection and a little deep thought, our original certainty seems to vanish as quickly as it appeared. This is the whole point of philosophy, to test our everyday assumptions against logical reasoning. This is not to say gut reactions and common sense are wrong. They are often right on the mark, but if we never examine our believes, we will never be able to really know anything.
Some great examples of these simple seeming conundrums are questions such as does God exist, can we trust are eyes, is it okay to tell a lie, is movement possible, and so on. All of these questions seem to have a yes or no answer and most everyone will already have an answer in mind. The point of the philosophical conundrum is to challenge ourselves to think about our believes. Our preconceptions maybe right or wrong, but unless we think about why we have this beliefs, we will never think more clearly.
Some people say that these philosophical questions are the type of questions that simply have no answer. An example of a question without an answer would be something like what does the number 14 smell like? Even though it is possible to make a question that can't be answered, these fundamental human questions, is there a God, are physical objects real, and so on, must have answers. If they didn't humans could never know, believe, or appreciate anything.