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Mathematical Games, Toys, and Puzzles

Look, my first award! Many thanks to Planet Science for picking this as their Site of the Day for April 26, 1996. (Unfortunately, you need to register to see their stuff.) While you're here, take a look at some of my other pages, too.

Sorry about the dust. Several of these pages have moved or died in the last few months, and there's lots of new stuff I need to add, but I've been busy with my real job. Thanks for your patience.


Combinatorial Games

Mathematicians use the words "game theory" in two different senses. The more common sense of the word includes things like the Prisoner's Dilemma, poker, the New York Stock Exchange, or other "imperfect-information" games. Research in this type of game theory makes a lots of money for a lot of people, and has even resulted in a few Nobel prizes. An introductory sketch is available at Drexel University.

Those aren't the kind of mathematical games I like. Combinatorial game theory tries to analyze the outcomes of "perfect-information" games like Nim and Tic-tac-toe. More difficult real-world examples are Hex, Reversi, Mancala, Checkers, Chess, Shogi, and Go. Nancy Casey has a page full of examples. (Unfortunately, all of the beautiful mathematics has been omitted, presumably because it wouldn't be understandable to a nine-year old!)

For a more thorough introduction, see On Numbers and Games by John Conway or Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John Conway, and Richard Guy. ONAG sets the foundations and wanders further into the mathematics; Winning Ways focuses more on actual games.

Game Theory (and Game Theorists)

Actual Games

Other Fun Math

What? Isn't all math fun?

Silly Math!

What? Isn't all m... Never mind.
All mortals must pay homage to Eve Andersson, green-skinned Web goddess from the planet Gragel. Nobody loves pi like Eve, but many foolish people try anyway. [Note hidden in Eve's homepage: "This photo was taken with a Polaroid Captiva camera which doesn't do a very good job of capturing true colors. In reality my skin is a lighter, more feminine shade of green."]
My Erdös number is three, but I don't have a Bacon number. I'll give a dollar to the first person who can name someone other than Steven Hawking with both a finite Erdös number and a finite Bacon number.

I'd really love to see a page of Marder numbers! (Larry Marder is the nexus of all comic book realities. Unfortunately, he also appears to be the nexus of all ugly Web pages.)

Here's everything you always wanted to know about everybody's favorite random number of yellow pigs. Don't believe Douglas Adams - the real answer is 17!
Archimedes Plutonium (also known as Ludwig Plutonium) believes that the entire universe is contained in the 94th electron of a Plutonium-231 atom. He also claims to have proved or disproved Fermat's Last Theorem, The Four-Color Theorem, the Riemann Hypothesis, the Poincaré Conjecture, Kepler's sphere-packing conjecture, the Goldbach conjecture, the existence of odd perfect numbers, the infinitude of twin primes, Cantor's continuum hypothesis, and Gödel's incompleteness theorem. You can read his regular diatribes/ rants/ prayers/ hymns on several Usenet newsgroups, including sci.math and alt.sci.physics.plutonium.

Jeff Erickson ( 27 Jun 96