PROVIDENCE, R.I. — Matt Cline wasn't even born when the Rubik's Cube hit the market in 1980 and became a worldwide fad. But the multicolor toy is the 20-year-old's constant companion, giving him a way to pass the time or compete with his friends.

"If I'm on an airplane and doing it, I almost always have somebody next to me ask about it,” said Cline, a student at Brown University , whose best time is 53 secon...