prediction paradox

The teacher and the class know that the last day of term is Friday. A week before, the teacher tells the class that before the end of term there will be an unexpected examination: the pupils will not know, the evening before, that the examination will occur on the following day. It seems plain that the teacher can set such an examination. But the bright pupil argues as follows. The examination cannot be on the final Friday. For then we would know, on the Thursday evening, that it had to be on that day. So the teacher's effective period, within which the examination must be set, ends on the Thursday. But then we know, on the Wednesday evening, that (since Friday is already excluded) it must be on Thursday. This contradicts the condition again. So the teacher cannot wait until Thursday. By similar reasoning we can show that there is no day on which the examination can be set.