A teacher announces to his students that he intends to give them a surprise examination. That is, on one of the next five (let us say) days he will give them an examination and they will not know which particular day it will be. He wants it to be a surprise, and so if on the morning of the examination the students can display knowledge that it will be that day he will cancel the examination. A bright student claims that the examination is impossible. Clearly it cannot be saved for the last day, for there would certainly be no surprise then. But similarly it cannot be given on the second last day, because if it was not given on the first three days, then on the morning of the fourth day the students, knowing that it cannot be given on the last day, would be able to predict that it must be the fourth day and so there is no surprise. And so on. At which point the teacher either forgets about the examination, or else, perhaps more wisely, goes on with his plan to have a surprise examination and succeeds.