From a review of William Lowell Putnam Mathematical Competition Problems and Solutions : 1938-1964 (out of print)
"I found the characters somewhat flat. Why, for example, does the set N choose to define himself in such narrow terms? Has he no dreams, no fantasies, no weaknesses, nothing but a recursive definition? Many of the characters had similar problems; I had difficulty relating to the motives behind some of their self-simplifying actions."

Consider the first sets in any book on set theory.  They doubtlessly have lots of complexes about whether they are well defined or not.  Usually, their good friend K = {the set of all sets which are not members of themselves}has just been killed off just because he was a bit paradoxical.  They have to deal with  as a neighbor, who is on the vacuous side.

Frege, who developed much of Set Theory in 1893, wrote "Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished."  Well, how did the sets feel?  Bertrand Russell sends over this K guy, and suddenly the world world is collapsing.  Good friends are zinging out of existance left and right.  It's as if gravity suddenly disappeared. You might want to ponder the Zermelo-Fraenkel Axioms to get a true feeling of what the set N has to put up with.


Here's a bit of fun I'm hoping to modify into a solvable problem.  Have I succeeded yet?  If so, send the answer, otherwise help me to modify it more.

There are three doors on a remote island.  By two of the doors, there is a native standing.  One native always tells the truth, one always lies. By the third door stands Monty Hall.

The natives have words for yes and no.  They are "ra" and "ta," but you don't know which is which.

The natives, of course, come from villages where each person has either a red or a green dot on their foreheads.  If a native discovers his or her color, then that native, out of civic duty, kills {his,her}self the next day at noon. 6 days ago, Monty Hall visited each village, proclaiming "I see a red dot," in the truthful village, and "I do not see a red dot," in the village of liars. (He was lying, of course; he just wanted to be consistent with the local customs.)

One of the natives drives a Toyota and the other an Oldsmobile.  Monty Hall recently traded a barometer for one of these cars.  The native that drove the Toyota is the island ruler who has a beautiful green-dotted truth-telling heir apparent who has not yet killed {him,her}self.  The other native owns a tiger.  At least one of these natives is male.

Behind the three doors are (not necessarily in this order):
1. a viscious, deadly tiger who always kills the person that releases him.
2. a car containing twelve coins (one fake) and a scale
3. a {lady,prince} you love entertaining the members of U2 with a flashlight.

Monty Hall, of course, will open the door not containing U2, then give you the option of switching doors.  With one question, can you become the new ruler and kill Monty Hall in the process?