Arabbit.387
net.math
utzoo!decvax!duke!chico!harpo!vax135!lime!houxg!houxi!ihnss!eagle!mhtsa!alice!rabbit!ark
Mon Mar 15 11:50:32 1982
Favorite Paradox
My favorite is sometimes called the executioner's paradox, but to make
it less gory, I am going to phrase it in terms of an exam.

The first day of class, the professor says: "There will be a surprise
exam some time before the mid-term, which is on November 4.  You will
not be able to predict the date in advance."

You reason as follows:  The exam can't be November 4, because he said
it would be before November 4.  It also can't be in the last class
before November 4, because if we come into that class and haven't had
the exam up to then, we can predict when it is going to be because
there is only one possible date left.  Assume the class on November 4
is number n.  We have ruled out numbers n and n-1.  What about n-2?
Well, if we come into class n-2 and haven't had the exam up to then, we
must be about to have it in class n-2, because we have ruled out n and
n-1.

By applying this reasoning enough times, you can rule out every class
period for the surprise exam.  Thus if the professor keeps his word,
the exam cannot be given at all, because there is no date it can
possibly be.

Where's the paradox?  Well, you walk into class October 7, and the exam
is waiting for you.  Boy are you surprised!  It seems that the
professor kept his word after all...