The answer is that this is something of a trick question brainteaser, or a paradox. This can be seen by following through the logic that the sentence is either true or false, and seeing what happens in each case.
If you can prove the sentence is true, then the sentence is false. If you can prove the sentence is false, then it is true. In this way a paradox is created.
What is the solution to the puzzle? Well, there is no direct answer to that as it is a paradox and is self-referential in a way that seems to admit of no true or false answer. One way out is to say that the sentence appears meaningless or has no definite meaning, and get out of the problem by admitting of a potential third possible logical state to a question rather than simply having to have a true or false answer.