When Things Can't Be Answered

These two sentences are from Plato and a Platypus Walk Into a Bar...Understanding Philosophy Through Jokes. What do you make of them?

True or false: This sentence is false.

If a man tries to fail and succeeds, which did he do?

In the first sentence, if the sentence is true that it is false, then that means the sentence is false that it is false, because then it is admitting that the sentence is false, but the sentence itself is false, so the sentence is true. This isn't the conclusion, however, because then you wind up where you started at. The same goes if you say that the sentence is false, because then you would be saying the sentence is false in saying it's false, which has to mean the sentence is true, but that wouldn't make sense, because you said the sentence was false in the first place. This doesn't have a proper answer.

In the second sentence, the man could have succeeded in the subject, and failed in failing, or he could have succeeded in failing. You can't conclude properly here either, because he could have failed his subject, or succeeded.

Do you have an answer to them?