Conquering Chaos

Can you conquer chaos? To play the game click here.

In Fractal Geometry, "Chaos" can be used create amazing images. Rober Devaney of Boston University has created this game to help his students understand this process. To find out more about The Chaos Game click here. To find out more about the wild world of Fractals, explore his site, which the link takes you to - or just play the game and have fun!

Towers of Hanoi

To play the game you see below click here. It's called The Towers of Hanoi. A history of the game is given below the picture. When you go to the site where you can play it, you can choose how many disks to use, and you can also have the computer solve it for you if you get frustrated!



According to Math Around the World by Lawrence Hall of Science :

"The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might have been used for the mental discipline of young priests. Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important provisonal large disk could never be placed on top of a smaller one. The priests worked very efficiently, day and night. When they finished their work, the myth said, the temple would crumble into dust and the world would vanish."

Nim Game

To play the version of the game of Nim pictured below, click here. (Here is another interactive applet for Nim.) Nim is an ancient game. There are many ways to play. In some versions the person who takes the last object (or number) is the winner and in other versions that person is the loser. It is thought to have originated in China; the earliest references to Nim in Europe date to the 1400's. It is often played with whatever objects are at hand (pebbles, toothpicks, matches, coins), but it can also be played verbally, without objects, as desribed below.




In order to play Nim verbally, find a partner and choose a number that you will count up to. You also need to choose the maximum amount of numbers you can count off at a time. For example, let's say you and I are playing, and we decide to count to 21. We also decide we can say up to three numbers at a time. I might start by saying: "1, 2, 3," and you might then say "4, 5." I might follow up with "6," and you might say: "7, 8, 9." We could continue in this way until we got to 21, and the person to say "21" loses the game.

This is a great game for a road trip, and there is a very straightforward strategy for winning every time (no matter what the ending number or the maximum amount of numbers chosen). Can you figure out the strategy??