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.)
(In reply to
re: not true by Bruno)
Not quite Bruno:
We eliminated Friday DUE TO THE FACTS that there are
No remaining days to hold the exam (no available days after Friday), and
If the exam hasn't occurred up until this day, it must occur on this day (negating the surprise).
In short, these two "facts" hold true RECURSIVELY. Once we've ruled out Friday, these two SAME FACTS apply to Thursday. Then, now that we've ruled out Thursday, these two SAME FACTS apply to Wednesday. And then we can apply them to Tuesday and Monday.
So, we *can* eliminate the other days using this process.
:)
P.S. The remainder of the argument continues (as has been expressed earlier)... with the notion that since all the days have been eliminated as possibilities, the professor can surprise them by holding the exam on any day.
re(2): not true
