The Puzzling Professor Pentomino

A mind-bending game inspires an unlikely artistic vision.

By Cheryl Ross

Guenter Albrecht-Buehler first got hooked on pentominoes about 20 years ago, when a puzzle in Scientific American caught his eye. He spent nearly 15 hours trying to fit the 12 rectangular shapes into a three-by-five-inch box. When he finally succeeded he was elated, exuberant. Pentomino puzzles were all the rage back then. But long after the fad had died down, Albrecht-Buehler was still addicted. In seven years he filled up a fat notebook with 900 possible combinations.

Pentomino rhymes with “domino,” and just as a domino is formed from two contiguous squares, a pentomino is formed from five squares. The five squares can be configured into 12 shapes, each named for a letter of the alphabet that it resembles. There is no mathematical formula to help you solve a pentomino puzzle. You just have to figure it out.

Albrecht-Buehler sets 12 wooden pieces and a rectangular box in front of me. I’m supposed to fit the pieces into the box. “In contrast to normal puzzles where you have a picture that orients you, here you have nothing,” he says. “You have absolutely no idea where any of the pieces go. Put the first 11 in there, and then you realize this is totally wrong. And then you begin to rearrange them, and the point is that they don’t flow. You make one rearrangement, everything repatterns.”

After about five minutes, I’ve managed to fit three pentominoes into the rectangular box, but only because he’s flashed me a cheat sheet. “I’m one-fourth done,” I say.

“Actually, we’re not even one-fourth done,” he replies. “The possibilities of placing these in there is not a fourth anymore. It will take you about three days before you have this solution, if you’re persistent and don’t give up. When you have this after three days, and it’s really in there, you’re exhausted and fascinated by the fact that everything fits–everything that never fit for three days. You’re convinced that this is the solution. A very human reaction. But it isn’t the only solution. There are 2,339 possibilities!”

About 13 years ago, Albrecht-Buehler took his obsession one step further and began creating pictures with pentominoes, transferring them to 32-by-48-inch slabs of plywood. The 55-year-old professor works in the basement of his Wilmette home, surrounded by more than 140 of his geometric mosaics. A single picture can take him as little as a month or as much as eight years before he’ll commit it to plywood. He refuses to display his work upstairs. “That’s not my style,” he says. “As a scientist I play with experiments, solutions, testing, ‘Can you do this? Can you do that?’ I’ve never looked at myself as an artist. I have no idea what this is.”

Albrecht-Buehler’s a professor at Northwestern University Medical School, where he stirred up controversy in the scientific community with his discovery that cells have “eyes” that can detect objects in infrared light. Though cells are his forte, he received his doctorate in physics in Munich, Germany. Now, despite his protests to the contrary, he’s begun a second career as an artist. A friend of his wife’s told the curator of a local gallery about Albrecht-Buehler’s pentomino pictures, and now his mosaics are displayed at the Fine Arts Building Gallery. The show, called “Logical Art and the Art of Logic,” continues through May 31 in suite 433. Albrecht-Buehler explains the history of pentominoes on his Web page (http://pubweb.acns.nwu. edu/-gbuehler).

He likens his pictures to tonal music, the Bach he’s played on the violin since he was a boy. Just as 12 halftones comprise a scale, Albrecht-Buehler uses the 12 pentomino shapes to construct his pictures. He uses all-natural colored woods to create the pentominoes, making sure the edges are extremely sharp, and fits them into 32-by-48-inch panels of 1,536 squares because the constraint forces him to solve patterning problems.

The metric quality of Bach’s music and his use of motifs and themes inspire Albrecht-Buehler in composing his pentomino pictures. “You just begin with something,” he says. “Most famous music compositions have very simple motifs. The composer links the pathway of this motif with pathways of others. So the motif changes along the way. But you could take this changed motif and begin with that again. So when I write patterns, I do just that. I begin with a relatively harmless thing, like saying, ‘Can I put these three U’s together? How many ways can I put them together in three dimensions?'”

Some of his pictures include impossible objects that can’t exist in nature; the professor likens them to dissonant musical passages. And in one picture, a blossoming rose reaches up from a landscape of interlocking geometric forms, suggesting the wild freedom of some musical sequences. “It really doesn’t matter how I do it,” he admits. “If it doesn’t work–if you, looking at it, don’t like it–then it was for nothing. The whole point is that people looking at this don’t have to know what pentominoes are, don’t have to know what the thinking process is. What I want people to do is follow these progressions of shapes and like them.”

Art accompanying story in printed newspaper (not available in this archive): Uncredited photos of Guenter Albrecht-Buehler and “The Monkey and the Rose”.