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.)

You guys are forgetting the fact that we can eliminate Friday only due to the fact that the teacher hasnīt applied the test on the other days. If we eliminate Friday by this process and we want to eliminate Thursday the same way, we must now include Friday back in the days that the test is possible.

I stand firm to being a paradox only if the test was to be applied on Friday:

The teacher hasnīt applied the test until Thursday. All the students assume he wonīt apply it tomorrow since they all know he HAS to apply it tomorrow, thus not being a surprise. Since everyone knows it wonīt be tomorrow, the teacher may then apply it on Friday. This is ONLY valid for Friday - making this a paradox.

Suppose the teacher comes and applies the test on Monday. Why canīt he apply it? Of course he can, because the elimination of Friday was ONLY DUE TO THE FACT THAT HE DIDNīT APPLY IT UNTIL THURSDAY. It would still be a surprise to some students.

And, finally, if the teacher comes on the first day of class and says: "This year, I will give you a surprise test." If we were to use this elimination process for all the days of the year, never would a teacher be able to apply a surprise test - in other words, surprise tests wouldnīt exist.

Hope this clears it up a bit. :)

Posted by Bruno on 2003-10-01 17:03:26