This is more of a logical paradox than math, but it's still rather interesting:
A prisoner has been sentenced to death, and the jailer tells him this: "You will be hanged one day next week between monday and friday inclusive, but you will not know which day until the morning of that day."
The prisoner is delighted to hear this, because he can logically deduce that he will not die from the jailer's statement. He can't die on Friday, because if he is still alive on Thursday afternoon, he will already know that he is going to die on Friday when it's only Thursday, and, according to the jailer, he can't know until the morning of the hanging. He then decides that if he is still alive on Wednesday, he can now only die on Thursday or Friday, but Friday was already eliminated, so he would know that he would die on Thursday, when it's only Wednesday. So now, he can't die on Thursday. Similarly, he rules out all the days of the week.
However, as the prisoner is waiting happily in his cell Thursday morning, positive he won't die this week, the jailer comes and tells him that the hanging will be this afternoon. Now the prisoner will be hanged unexpectedly, just as the jailer had originally stated. And the jailer's statement is valid again.
So was the prisoner right in his deductions that he can't die, when real life so obviously contradicts him???
