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The Waitress and the Mathematicians

I recently heard two stories on a LinkedIn math forum, under the topic of humor in mathematics. The first is a funny little story, which I first heard years ago. The second is a cute logic puzzle.

Two mathematicians, Tom and Joe, are in a restaurant, discussing the state of mathematical illiteracy in the general public. Tom goes to the restroom, and Joe calls over the waitress and says, "I'd like to play a trick on my friend. I'll call you over and ask you a question. I'll give you ten dollars if you answer my question with 'x squared'". She agrees, and takes the money. Tom returns, and sometime later Joe says to Tom, "I'll bet most people know how to find the antiderivative of a simple function". Tom disagrees strongly, and Joe says. "OK, I'll bet that our waitress knows the antiderivative of 2x. If I'm wrong, I'll pay for lunch. If I'm right, you pay." Tom says "You're on."

The waitress comes over, and Joe asks her, "Excuse me, miss, but do you happen to know the antiderivative of 2x." The waitress replies "Sure. It's x squared ... plus C".

Four mathematicians come into a restaurant together, and a waitress comes over, and asks "Would you all like coffee?". The first mathematician says, "I don't know". The second mathematician says "I don't know". The third mathematician says "I don't know". The fourth mathematician says "no".

The waitress, who is no slouch at logic, comes back with the correct number of coffees. How many coffees did she bring?

E21. Equiangular and Equilateral Polygons

A polygon is equiangular if all of its angles are equal. In particular, if the polygon has n sides, each angle measures (n - 2) * 180 / n degrees. A polygon is equilateral if all of its sides have the same length. It can be shown very easily that every equiangular triangle is equilateral. Of course, it is not true that every equiangular quadrilateral is equilateral. Any rectangle that is not a square provides a counterexample. Show that for every n > 3 there exists an equiangular n-gon that is not equilateral.