The way "groshing" works, explains its 17-year-old creator Mike Finn, is you take an integer, any integer, and send it through a function consisting of digits raised to a certain P power. When that new integer comes tumbling out, plug it back into the function. When you finally reach an infinitely repeating sequence of numbers, stop groshing. Thanks, Mike. No sweat.

For Finn, a senior at Lake Braddock High School in Fairfax County, there is nothing quite as exhilarating, or lucrative, as the numbers game. Last year Finn's mathematical talent earned him a two-week trip to London for the 21st International Mathematical Olympiad. This week he won a $10,000 scholarship to the college of his choice. Already, he is computing the odds for higher stakes.

"It would be nice to win a Nobel Prize," said Finn this week after placing third in the prestigious Westinghouse Science Talent Search, a national competition for high school seniors that has included three winners who later became Nobel laureates.

Finn was one of 40 whiz kids from 17 states who qualified for the 39th running of this annual contest at the Capital Hilton Hotel. Each of the contestants endured five days of interviews, punctuated by meals and sightseeing tours, for the honor of the games and the $91,500 in prize money and scholarships. For many of the prodigies, it was the first time they had ever been in the company of so many intellectual peers.

There were three local entries besides Finn. George Weinart, a senior at Germantown High School in Maryland, tried to lay a scientific foundation for the biblical parting of the Red Sea. John Mature, of J.E.B. Stuart High School in Fairfax County, concocted a chemical to rid chlorine of elements that might cause cancer. And Heather Dick, of Rockville High School in Montgomery County, put together a study of the relationship between white blood cells and germ particles. None finished in the top 10, but each received $500 in cash.

"The project is really just an admission ticket," said Finn, sitting in his hotel room the day after the winners were announced, watching a bad, mid-morning movie and trying not to fall asleep. "Once you get here the project doesn't mean a thing. They're (judges) looking for creativity. Potential. A lot of it is luck."

Finn has instant and total recall. But so do a lot of people. What makes him remarkable, says his high school math coach, is his ability to relate everything he learns into one, integrated system.

"I've had a lot of sharp students but none like Mike Finn. He's one in a million," says Lake Braddock math teacher Will Misner, who hasn't been able to teach Finn anything new since the eighth grade. "He knows 100 times more than I'll ever know. I think it's heredity."

Finn's father is a physicist for Mitre, a local research corporation. His mother is a former high school math teacher. His grandfather was a math professor. But Finn has no ambition to take up the chalk and follow them into the teaching profession.

"It doesn't pay enough and I think it could be a grind," said Finn, who refuses to play the bespectacled, absent-minded role that the world expects of its mathematical masters.

He is as much at home talking about basketball and baseball as cosines and logarithms. And while he enjoys the abstract tinkering with numbers and shapes, this high school senior is plotting his future on more rewarding ground.

"I know of two PhDs at the University of Maryland who specialized in relativity and quantum mechanics and are now in the piano tuning business," said Finn, who last year had the only perfect score in a Mathematics Association of America exam taken by 370,000 students. "I don't want that happening to me." CAPTION: Picture, Westinghouse winner Michael Finn, 17, of Annandale, won a $10,000 scholarship.