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

June 26, 2007

Hard Cash

What could you do for fun with some coins and a sheet of paper? That's all Bob Hearn, a graduate student at the Massachusetts Institute of Technology, needed to invent a new kind of puzzle. Here's an example.

Place four coins on the bottom row of circles (covering G, D, E, and R). This leaves the letters MARTIN exposed. Your challenge is to slide the coins along the paths joining the circles until the four coins cover the top row of circles (M, T, I, and blank), exposing the letters GARDNER. (By the way, Martin Gardner is the name of a famous math writer and puzzle expert.)

Sounds simple? The catch is that the coins can never be directly connected by a path. For example, you can't move the G coin initially because the only allowed move would put it next to the D coin. The D coin can move to the T circle but not to the A circle or the I circle. You also have to slide the coins one at a time, all the way from one circle to another. And, where paths cross, you can't switch from one path to the other.

Hearn has discovered that such puzzles can be surprisingly tricky. For example, it takes 25 moves to solve the MARTIN GARDNER puzzle, and Hearn has come up with puzzles that take more than 100 moves to solve. In fact, he's written a computer program that searches for the hardest puzzles of a given size.

Here's another one that you might like to try (below). In this case, you put coins on the black circles. Then you have to slide the coins along the paths until there is a coin in every starred circle. Again, you're not allowed to move a coin to a circle directly joined to another coin. You should be able to solve the puzzle in 28 moves.

Are these too tough for you—or not challenging enough? Try changing the rules or inventing your own sliding-coin puzzle. There are lots of possibilities. You can add or subtract paths or change the number of circles or coins. The tricky part is coming up with something that's fun and challenging but not impossible to solve!

Hearn's new brainteasers have inspired designer James Stephens to create a set of puzzles that he calls the "Meandering Monk Maze." You can try them online at

Muse, February 2006, p. 33.

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