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.)

I would like to propose an amendment to the solution that gives the students the benefit of the doubt. By concluding that they "know" that there will be NO test, the students have allowed for the possibility that the professor was lying. But certainly some of them would recognize "the class has decided (and are supposedly 100% sure) that there is NO test next week. Therefore the professor could give a test on any day and it would still be a suprise." So YES, the professor could give a test any day (as was stated in the solution) and it would be a surprise (as is defined), but the students would know that this is still possible, though the could not be certain since they've already allowed for the possibility of no test at all. That's probably a bit wordy...but my point is that the students would not be totally caught off guard (as seems to be implied in the solution). They would be SUSPECTING a test, just not 100% sure of it.

Posted by Greg on 2003-01-07 21:42:49