this is a classic paradox from Martin Gardner's Book of Paradoxes, which has a ton.
anyway, the lady says "You will eat my baby."
If the crocodile eats the baby, the lady predicted right, so he has to give it to her. But if he gives it to her, she predicted wrong, so he gets to eat the baby... but then she will have predicted right. An endless cycle. Except it's answered easily:
I just said this: "If the crocodile eats the baby, the lady predicted right, so he has to give it to her." So he gives it to her, THEN realizes she predicted wrong. by that time, though, she's running away with the baby, and there's nothing the croc can do.
that's not what Martin Gardner wrote, but thats how i think of it