An olympics with geometry problems instead of 100-meter dashes, quiet classrooms instead of noisy stadiums, high school math stars instead of star athletes opened yesterday at Georgetown University.

It is the 22nd, International Mathematical Olympiad, the world's most prestigious math competition for high school students. For the first time the contest is being held in the United States, with 185 students representing 27 countries, ranging from the Soviet Union and Romania to Tunisia, Israel and Brazil.

The eight-member American team includes one student from the Washington area, Brian R. Hunt, a 15-year-old junior at Montgomery Blair High School in Silver Spring, who tied for first place lat winter in a qualifying exam taken by 422,000 students nationwide.

"So far it's been easier that I expected," Hunt said yesterday after finishing the first 4 1/2-hour part of the two-day written exam. which tests problem-solving ability in complicated algebra and geometry but does not require calculus or more advanced math.

"I kind of enjoy the competition even though I don't know if there's really too much point to it. It' mainly a game. But a lot of people think there's more to it."

Indeed, even though the contest is quiet -- with few spectators invited to the opening ceremony and none allowed in the classrooms where the tests are held -- the competition is intense because the reputations of national school systems are clearly involved.

"It's supposed to be between individuals, but everyone taking part in these things can count," said Mas ya. Sobel, president of the National Council of Teachers of Matematics, one of the sponsors of the event. "So we all keep track of the teams. It's like the Olympics [in sports], where everyone keeps team standings."

In the most recent Math Olympiad, held in England in 1979, the Soviet Union finished first, as it had wight times before, with Romania second. The United States was fifth.

Last year, shortly after the United States decided to boycott the Moscow Summer Olympics, the Soviet Union and several of its allies quietly withdrew from the Math Olympiad and the contest wasn't held for the first time since it started in 1959.

"The students from all countries love this competition," said Samuel L. Greitzer, chief organizer of the Olympaid and chairman of the contest jury. "They like it as much as any kid would like soccer or basketball or, if they ever have it again, baseball. . . .

"These students go into scientific careers and their knowledge of math is invaluable there," said Freitzer, a retired mathematics professor from Rutgers University who has trained American teams for the contest since the United States first took part in 1974. "I consider these students a natural resource rarer than uranium."

Yesterday as he left the examination room in dark blue jogging shorts and a light blue T-shirt, Hunt looked more like a high school student on summer vacation than a natural resource.

"I didn't want to get too hot," he explained about his clothing, though the classrooms where the test was taken turned out to be air conditioned.

Hunt's education sinced he entered first grade at Montgomery Knolls Elementary School has been as unorthodox as his test-taking clothes.

"Early on, the schools figured out they couldn't do much for him academiclly," said Hunt's mother Janet, an associate professor of sociology at the University of Maryland, where his father also teaches sociology. "They just let him wander around and do whatever he wanted to do, so he hooked up with some kids a little older than himself and stayed with them."

When he was 11 and scored 780 on the math part of the Scholastic Aptitude Test (out of a possible 800 points), Hunt started taking calculus courses at the University of Maryland. Since then he has moved on to graduate-level work, said professor James Yorke, one of his math teachers at Maryland, though he has stayed in Montgomery Blair High School for courses outside math and science. He is on Blair's varsity swimming team as well as its math and chess clubs.

Hunt said he isn't certain he'll be able to graduate from high school next year because he hadn't taken enough required courses. But Yorke said that probably won't matter because the University of Maryland would be willing to let him enroll for a master's degree even without a high school or college diploma. "After all, he has been working at the M. A. level for some time," Yorke said.

"I am probably more advanced than most," Hunt explained about his math education. "But that's not particularly useful in this competition."

The math he did need, which calls for creative proofs with rigorous logic and reasoning, not calculus or elaborate theorems, was taught at a special four-week training session. The eight members of the U.S. team went to the Military Academy at West Point for the intensive training, which would up last Wednesday when they joined the foreign Math Olympiad teams at Rutgers University in New Jersey for our days of resting, sightseeing and getting to know other contestants.

All the students came to Georgetown by bus Sunday afternoon.

While the contestants were in New Jersey, their team leaders assembled with Greitzer and an assistant at Mary Washington College in Fredericksburg, Va. There they decided on the contest's six questions and translated them into 18 languages.

"We're concerned with security," Greitzer said, "so we make it difficult for [the leaders] to make a phone call to their teams. We don't tell them where to call and we keep them away from the team until after the examination is over."

The students write out the answers in eight rooms each containing no more than one contestant per country. Each team leader does the preliminary grading of his own students' answers. But Greitzer said the grading is kept uniform by a cadre of 18 coordinators, picked by the United States as the host country, who have authority to assign points, subject to appeal to the jury which is made up of all countries participating.

"We haven't had any real trouble" with the fairness of the grading, Greitzer said, "and I don't expect any."

The National Science Foundation is paying most of the $140,000 cost of the Olympiad, which concludes with an awards ceremony Sunday when winners will be announced.