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.)

This paradox may be explained as follows:

The exam cannot be given on the Friday, as by the end of class on Thursday, the students will know that it must be given on the Friday. If it cannot be a surprise on Friday, then it cannot be a surprise on the Thursday, as by the end of class on Wednesday, the students know that it must be administered on the Tursday to be a surprise. (Since it cannot be a surprise on the Friday.) Using similar reductive thinking, we can work back to Monday's class, without it being logically possible for the exam to be a surprise. Remember, this is a paradox, and as such it is counterintuitive. It is possible that the 'paradox' arises from a misunderstanding of the word 'surprise' as it relates to this question. Since by 'surprise' we generally mean something not anticipated, it is disingenuous to think that the exam could be a true surprise on any day (as the students are surely expecting it). Once this semantic power is removed, the force of the establishment of the paradox is reduced.

Posted by lone on 2004-12-03 07:30:11