A Fairfax County high school student has scored a perfect mark in the two-day International Mathematical Olympiad in Belgrade, Yugoslavia, helping the U.S. team to its first victory in the events.

Randall Dougerty, a senior this fall at W. T. Woodson High School, received a perfect mark of 40 in the July 3-4 competition between high school-aged teams for 17 nations.

Dougherty, 16, was one of two U.S. contestants among the five who made no mistake on the rigorous test of mathematical logic.

That helped the U.S. to a total score of 202 from its tight-member team, topping the Soviet Union's 192 and Great Britain and Hungary, each with 190.

Dougherty had placed second in each of two rounds in the Sixth U.S.A. Mathematical Olympiad sponsored by the Mathematical Association of America. About 365,000 students had entered that competition.

Dougherty also was a member of the U.S. team that finished third last year behind the Soviet Union and Britain in Austria.

This year the U.S. team went into training for three weeks at West Point, N.Y., before flying to Europe for final preparations for the event. The team will return to the United States later this week.

Dougherty, the son of a Navy captain, has lived in six different states and attended classes in six different school systems. He could multiply three and four digit numbers in his head when he was 4, accoridng to his mother, Judy, a real estate agent. The family moved to Fairfax County when Dougherty was a sophomore.

After his high finish in the U.S. contest, Dougherty said that in solving the complex problems he tooks for a trick solution, something that would take it real simple . . .The elegant solutions are almost always the simple ones. I get a good feeling out of doing it."