## MatheMUSEments

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

## April 15, 2007

### Puzzling Art

An art gallery isn't the first place you would think to look for math, let alone a mathematical puzzle. But Barry Cipra, a mathematician and writer in Northfield, Minnesota, found a puzzle in a set of large drawings by American artist Sol LeWitt.

LeWitt is famous for the use of simple patterns and basic geometric shapes in his drawings, sculptures, and paintings. In 1973, he composed an artwork that consisted of 15 squares. On each square, he drew a horizontal, vertical, or diagonal line, or some combination of these lines. The 15 squares, arranged into a four-by-four grid with one blank space, represented all possible combinations of such lines.

When Cipra first saw this set of drawings, he was intrigued by how his eye automatically tried to connect the lines from one square to the next. In LeWitt's arrangement, however, none of the horizontal, vertical, or diagonal lines actually went from one side of the grid to the other.

Cipra asked himself if it would be possible to rearrange the 16 squares (including the blank one), without rotating any of them, so that the horizontal, vertical, and diagonal lines did go all the way across the grid.

Straight Lines in Four Directions and All Their Possible Combinations: The math problem. Make a copy of these squares on a sheet of paper, then cut out the squares to see if you can solve the puzzle. The rule is, you aren't allowed to rotate the pieces to find a solution. Be careful!

Using square pieces cut from stiff cardboard, Cipra came up with a solution. He later used math to prove that there are exactly three completely different solutions to the puzzle. Can you find one? Or all three?

The question is, could LeWitt himself find a solution to the LeWitt puzzle? Did the artist even know he made a puzzle?

Muse, February 2001, p. 34.