MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

October 10, 2007

Mystic Puzzler

Lots of computer games have you whacking monsters as you struggle to find better weapons and power up. Some games, however, rely on puzzles more than single combat. If your game is one of the puzzling kind, trial and error might get you by, but a bit of logic or mathematical knowledge will often speed you on your way.

Near the beginning of the game Myst, for example, you encounter a contraption that has three levers and three stacked dials, each one reading 3.

Pulling the levers reveals that each of the dials is three sided. Rotating a dial reveals other faces, numbered 1 and 2. If you've been paying attention to other clues in the game, you realize that your task is to use the levers to rotate the blocks until they read 2, 2, 1 instead of 3, 3, 3.

But how do you do this?

Jessica Sklar of Pacific Lutheran University in Tacoma, Washington, is both a mathematician and a gaming geek, and she especially loves games that contain puzzles. Here's how she would tackle the Myst puzzle.

Let's label the levers A, B, and C. Experimenting, you soon discover that pulling lever A leaves the top block unmoved and turns the middle and bottom blocks to show the next face. So, if you start with faces 1, 2, 3 (from top to bottom), the new pattern after pulling lever A would be 1, 3, 1. Pulling lever B leaves the bottom dial unmoved and rotates the top two dials. Lever C resets the blocks to their original 3, 3, 3 pattern.

It turns out there's no way to get from 3, 3, 3 to 2, 2, 1 by pulling the levers. You have to pull lever B twice to get the top block from 3 to 2. In so doing, you also move the second block to 2. To move the third block to 1, however, you have to use lever A once. And that also moves the second block—back to 3. No combination of moves works, and Sklar can prove mathematically that's absolutely true.

So there has to be a trick. Indeed, if you play with the levers a bit, you find out that you can give the middle block an additional turn by holding down lever A or B.

Now, there's a solution. Pull lever A once, lever B twice, then hold lever B down after its second pull just long enough to turn the second block two more times. Pretty sneaky! You hear a grinding noise, and the gear at the bottom of the contraption opens, giving you access to a book that allows you to travel in a different world.

Many computer games contain logic and math puzzles. You'll find them in Myst, Timelapse, and Trinity—and even in SpongeBob SquarePants: Battle for Bikini Bottom. You never know when some math may come in handy.

Muse, October 2007, p. 36.