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.)
As a sometime Math teacher, I can say with absolute certainty that no matter how clear the proffessor may have been in his instructions about any forthcoming surprise (or other unsurprising) tests, there will always be some (worryingly large) percentage of students that will be utterly surprised, bewildered and even indignant that they have a test. Hence I don't think any class will ever be 100% certain about the timing of any test - or anything else for that matter. So he, and I, can always give surprise tests.
Math Classes and Surprises
