A professor tells his class that he will give them a surprise examination sometime next week.

For our purposes, an examination is considered a "surprise" if on that day, the class is not 100% sure that they will get an examination. (If they only suspect it, the examination can still be a surprise.)

Having given the class this warning, is it still possible for the professor to give them a surprise examination next week? (Assume that he will not give them an exam if it will not be a surprise.)

Here's an indirect proof that he can't hold a surprise examination any day of the week. (This is assuming every student in the class thinks the same way.)

Suppose the day was Friday. Then the class would not have this exam Monday through Thursday. Since the only day left to have an exam that week would be Friday, it can't be Friday. This is a contradiction, so we can RULE OUT Friday. In other words, Friday is as unlikely to have it as Saturday; the statement "I will have it Monday, Tuesday, Wednesday, Thursday, or Friday" logically equivalent to "I will have it Monday, Tuesday, Wednesday, or Thursday"

Now, since we have proven that the two preceding statements were logically equivalent, we can proceed on with Thursday. If the class hasn't had the quiz by Wednesday, the class will know it's Thursday. This means the quiz will not be given Thursday. So, we can RULE OUT Thursday.

This can be continued on to rule out Wednesday, Tuesday, and Monday. So he can't give it next week.

Posted by Gamer on 2003-09-30 17:20:40