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Math Chat: Halloween Card Games And Spinning Sprinklers

Old challenge

An old-fashioned water sprinkler with S-shaped spiral arms is propelled counterclockwise as the water spurts out. Which way will it turn if you place it upside down under water and have it suck water in?

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In the best and winning answer, Sirius Fuller explains that the sprinkler "will not turn at all. It may vibrate, but it won't spin. The reason I know this is that I read a book entitled 'Genius' by James Gleick. It's about the life of [famous physicist] Richard Feynman.

"At one part it tells how Feynman, and several others, were trying to solve the problem that you put forth.... After much debate Feynman went to a lab and put the sprinkler in a sealed glass tank mostly filled with water. The sprinkler had a tube attached to it going out of the tank, through the seal, and into a different container.

"He then forced air into the top of the tank so that the water would be forced down into the sprinkler and up the tube. The sprinkler started to vibrate. He increased the amount of air going into the tank, yet the sprinkler did not spin. Feynman continued to increase the air pressure until the glass tank shattered. Besides getting him permanently banned from the lab, it also proved what he initially suspected, which was that the sprinkler would not move. After thinking about it, he put forth the hypothesis that water was going into the sprinkler from many different angles. The different forces canceled each other out, and thus the sprinkler would not spin."

New Halloween challenge

Ralph Thomas proposes a new card game for you and an opponent for Halloween. Each hand, a goblin deals both players a certain number of cards. The highest card wins (i.e., ace beats king, two aces tie). If you win you get two points; if your opponent wins, he gets just one point. (You have an advantage.)

Do you prefer to use a regular deck, a double deck or a pinochle deck (which has two of each card from 9 on up to ace)? How many cards would you like the goblin to deal out each hand? Do you prefer four or eight hands in the tournament?

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* Send answers, comments, and new questions to:

Math Chat

Fine Hall

Washington Road

Princeton, NJ 08540

or by e-mail to:

fmorgan@princeton. edu

Professor Morgan's homepage is at www.williams. edu/Mathematics/fmorgan