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.)

Ok, my first try just might not make sense...so I'll try again. This time by using a possible diaglogue between the students to make my point? "We KNOW that the test won't be on Friday, because then it would not be a surprise (at this point the students have assumed the professor is not lying about giving a test). So it must be M T W or Th...But, then it can't be Th. because (etc. etc. until Mon). SO THERE IS NOT A TEST! But wait!! We assumed there is a test (that he is NOT lying) but concluded that there is not one (that he is lying). So which is it...we just don't know. Maybe he's lying, maybe not. And because we don't KNOW which it is, then we can not rule out Friday (which led to Th. W T M). So the professor may still give us a test, on which day we do not know, or he may not give one at all." Whew...sorry so lengthly, but my point is that the students are not caught completely off guard, as it seemed to be implied in the solution, just that they can not be 100% certain and are therefore suprised (accourding to the definition). Anyways, take it for what it's worth...probably not much at all.

Posted by Greg on 2003-01-07 21:59:04