Uptown Girl

A man has two girlfriends, one who lives uptown and the other downtown. He likes them equally, so he lets the trains decide which he will visit: He arrives at the train station at random times and takes whichever train arrives first.

Over time, he finds that he’s visiting the uptown girlfriend much more often than the downtown girlfriend, even though uptown and downtown trains arrive at the station equally often. Why?

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Water Battle

http://commons.wikimedia.org/wiki/File:Early_action_Water_Battle.jpg
Image: Wikimedia Commons

An odd number of people armed with water guns are standing in a field so that all the pairwise distances are distinct. At a signal, each shoots at his nearest neighbor and hits him. Prove that one person doesn’t get wet.

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Six Choices

On a multiple-choice test, one of the questions is illegible, but the choice of answers is listed clearly below. What’s the right answer?

(a) All of the below.
(b) None of the below.
(c) All of the above.
(d) One of the above.
(e) None of the above.
(f) None of the above.

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Paint Scheme

paint scheme puzzle

How many colors are necessary to paint the squares of a chessboard so that no bishop can move between two squares of the same color?

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Fowl Play

http://commons.wikimedia.org/wiki/File:Julius_Scheuerer_H%C3%BChnervolk_und_ein_Truthahn.jpg

From a 1947 competitive examination for high school seniors conducted by Stanford’s math department:

My grandfather’s papers included an old invoice:

72 turkeys $-67.9-

The first and last digits are illegible. What are the missing digits, and what was the price of one turkey?

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Rolling

http://commons.wikimedia.org/wiki/File:Rumble_Seat_(PSF).png

I drove this car 20,000 miles and used five tires equally in accumulating the mileage. How many miles’ wear did each tire sustain?

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