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Arabbit.387 net.math utcsrgv!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...

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