Once upon a time, at a prestigious Ivy League university, a professor of mathematics was perturbed by his students' lack of interest in the subject he was teaching. The professor tried and tried to make his students excited about mathematics but all the boys were interested in was football and beer and all the girls were interested in were the boys.

Finally, at his wits' end, the professor announced that henceforth, an "unexpected examination" would be given one day each week and that there would be no way any of the students would be able to predict which day the exam would come.

Now, Mike, the president of Alpha Beta Gamma, the most exclusive of the fraternities on campus, thought of himself as something of a logician and set about to predict what day the exam might happen.

"If I go to class Monday through Thursday and there is no exam, then I will know that the test will happen on Friday. It will not be unexpected, which Dr. Gauss assured us it would be. Therefore, he won't give us the test on Friday," Mike thought.

"But if he doesn't give us the test on Friday, he can't give it on Thursday, because it won't be unexpected," he went on. "Hmmm. This means that he can't give it on Friday or Thursday, and by extension, he can't give it on Wednesday, Tuesday or Monday. He must have been just trying to scare us. I'll bet he won't be giving us a test at all."

Imagine Mike's surprise when Professor Gauss offered the unexpected exam on Wednesday!

Where did Mike's logic break down?

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