Stewart Coffin of Andover designs geometric puzzles. He has been making puzzles for more than 37 years, creating about 223 designs. Top left, are some puzzles made by Coffin.

Stewart Coffin clears a space on his dining room table and sets down a small rectangular wooden tray. Beside it he lays four wooden tiles, two triangles and two trapezoids. The object of the puzzle is to fit the four tiles within the rim of the tray.

If you’re like most people, you start by fitting a square corner of a tile into a square corner of the tray.

Coffin, 77, leans forward in his chair, amused. It’s a trap.

“Your first mistake is putting a square corner into a square corner,” he says. “As long as you do that you’ll never solve this puzzle.”

Coffin, who lives in Andover, is one of the most famous mechanical puzzle designers in the world. He invented this seemingly simple puzzle called The Cruiser with techniques inspired by a magic show.

Like a magician, Coffin’s puzzle uses misdirection. He’s taking advantage of the fact that a person’s desire to fit corners into corners is so strong that they can’t resist it. Even when he tells them it’s wrong, many people can’t stop, he said.

“All your life you’ve been dealing with square and rectangular things, anywhere from city blocks down to things in a desk drawer,” Coffin said. “Well, some things don’t work that way. They just don’t work that way.”

Just when the solution seems impossible, Coffin takes over and clicks the tiles into place. Each tile fits at an angle, with not one square corner in a square corner.

“People get very upset about this,” he said.

This is just one of the puzzles Coffin plans to demonstrate in February when he speaks at a major scientific conference in Boston, the American Association for the Advancement of Science annual meeting.

Scientific conferences are not Coffin’s usual scene. He’s more at home at puzzle conventions, where he’s greeted as a celebrity, and on the craft show circuit, where he sold his puzzles for more than 30 years. Like many top puzzle designers, Coffin works intuitively, without any formal training.

“Mechanical puzzles are designed by just a handful of geniuses around the world,” said Peter Winkler, a mathematics and computer science professor at Dartmouth College. “And they don’t tend to be academic types.”

Winkler, himself an “academic type,” collects mechanical puzzles as a hobby. On a whim he decided to put together a panel of top puzzle designers to talk at the AAAS meeting. Creating and solving puzzles has a lot of relevance to mathematics, he said, even if official math credentials are not required.

Coffin was an automatic choice to be on the panel, he said.

“I don’t think I could exaggerate his reputation,” Winkler said. “He’s one of the greats. I think a lot of people would describe him as kind of the dean of American puzzle designers, one of the handful of top people in the world.”

You would never know it, talking to Coffin.

Man of many pieces

At 77, Coffin scaled back his puzzle-making business and now spends most of his time writing. Though he has authored several books on mechanical puzzle design and woodcraft — including “Geometric Puzzle Design,” published in 2007 by A.K. Peters — he is also writing memoirs of his years living on a subsistence farm in Lincoln, his wilderness canoe adventures, and even his life since moving to Andover in 1998.

Puzzle design is simply one aspect of his life, he said, and something he fell into by accident.

Coffin went to college for electrical engineering and got a job in the 1950s at Massachusetts Institute of Technology’s Lincoln Laboratory building computers, and then took a job in industry.

In 1964 he became disillusioned with his career and “dropped out” to start a business making canoes in his basement. He fathered three daughters and, a few years later, moved the family to a 9-acre farm in Lincoln, where they worked the land and he built a workshop for his canoes.

One day about six years later, while tinkering in his shop, Coffin got an idea for a puzzle. It was based on a memory of an illustration in a math book his father gave him. He made some epoxy prototypes of puzzles — a tangle of interlocking, notched hexagonal rods — and gave them to his girls. When their school librarian saw the puzzles, she put Coffin in touch with a local man who happened to be one of the few business agents in the United States who specialized in puzzles and games. Coffin’s puzzle design was licensed to 3M, and 100,000 copies were manufactured.

Solving the puzzle was so complicated that nobody at the factory could assemble them, Coffin’s daughter Tammis said. So 3M sent the puzzles to Coffin, and he paid his daughters and the neighborhood children a few cents per puzzle to assemble them in a tent on their lawn. They put together 20,000 puzzles in two weeks, Tammis said.

Tammis, who was 9 at the time, said she learned to assemble the puzzle with her eyes closed.

That first puzzle was so successful, and Coffin was so sick of the fumes from fiberglass canoes, that he changed the focus of his business to puzzles.

Unfortunately the deal with 3M turned out to be beginner’s luck. Coffin worked on new puzzle designs for a year without another license deal. So he taught himself woodworking and decided to manufacture the puzzles himself, selling them on the craft show circuit.

Though three-dimensional wooden puzzles now are a staple at craft shows, at the time Coffin’s puzzles were unlike anything else.

“Stewart Coffin has had such a profound effect on the design of interlocking puzzles that it is hard to remember the state of the art of interlocking puzzles ‘BC,’ before Coffin began in 1970,” said Jerry Slocum, a puzzle collector and founder of the International Puzzle Party, in a speech last summer honoring Coffin as the first recipient of the Nob Yoshigahara Award for lifetime contributions to mechanical puzzles.

“His designs and crafting of polyhedral puzzles began a whole new category of interlocking puzzles, which are also beautiful art objects,” Slocum said. “Some of these require simultaneous coordinate-motion to take apart and re-assemble.”

Coffin has been prolific, inventing more than 200 original puzzles in his lifetime. Many of them were commissioned and purchased by puzzle collectors for the puzzle exchange at Slocum’s invitation-only annual puzzle parties.

Coffin also freely shares his designs and techniques, so his puzzles are widely reproduced and sold all over the world.

“People who build puzzles, they know the Coffin puzzles by number,” Winkler said. “They’ll say, ‘I built a 23’ or ‘an 86.’”

A couple years ago, Coffin was bicycling in the Czech Republic wearing a T-shirt with a picture of a geometric puzzle on it. Somebody told him he should visit a particular store in Prague that was selling puzzles just like that. Coffin found the shop, and in the window were a few of his designs, made by a Czech woodworker. Inside there was a whole display case full of geometric puzzles. Coffin picked up one of his own pieces and showed it to the clerk.

“It was priced at 2,500 korunas, which was about $350,” Coffin said. “I said I made that puzzle in 1985 and sold it for $40.”

Part puzzle, part art

Before Coffin started designing puzzles, the typical interlocking puzzle for hundreds of years was composed of right angles, Slocum said. It was a rectangle or square or cluster of rectangular sticks that fit together at right angles. These puzzles were complicated to assemble and not particularly elegant to solve, Slocum said.

“What Stewart did is he changed the geometry completely,” Slocum said. “It’s almost like another dimension of mathematics: Rather than things that just fit in orthogonal (right) axes, things that fit in other skewed axes and at odd angles to make these beautiful polyhedrals.”

Coffin’s puzzles are shaped as multipointed stars, pyramids and angular balls. Though the structures look complex, the solutions are elegant and satisfying, Slocum said.

“His polyhedral puzzles, they’re beautiful three-dimensional sculptures, basically,” he said. “To create the structure from these bits and pieces of three-dimensional sticks is creating an object of art. You’re not designing it, but you’re creating this art by putting it together.”

There’s no magic here, Coffin said. Rarely did a new design come to him in a moment of inspiration. Most of them were the result of hard work and long hours of trial and error in the wood shop.

“For every one you see here, or listed, there were hundreds that just went into the stove,” Coffin said. “We heated our house with my mistakes.”

Coffin has been an innovator in designing other types of mechanical puzzles, as well, Slocum said. Lately he has been designing flat puzzles, like The Cruiser, with his innovative use of psychological trickery.

Slocum had Coffin make a flat puzzle based on similar principles to be Slocum’s contribution to the puzzle exchange at his party this past summer in Australia. It’s a simple-looking one called “Forfeit.” Like The Cruiser, it has four tiles that fit within a wooden tray.

Slocum liked it so much that he sent one to Martin Gardner, the legendary former math and puzzle columnist for Scientific American.

“Two weeks later he sent me this letter and said, ‘Who in the hell invented this damn thing? I’ve wasted two weeks on this,’” Slocum said.

That’s a high compliment for such a simple puzzle, Slocum said. And it illustrates why Coffin’s so good.

“One of his faculties that is extraordinary is to watch how people solve things and to be able to design it so that they are not able figure it out,” he said. “I don’t know of anybody else who has been able to do that successfully.”

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