66th Annual STS (2006-2007)
Finalists
Gregory Drew Brockman

NORTH DAKOTA
Gregory Drew Brockman, 18, of Thompson, submitted a mathematics project to the Intel Science Talent Search in which he studied the set of Ducci sequences, also known as the four-number game. To play the game, start with a sequence of four numbers a, b, c, d, and replace it with the sequence ¦a - b¦, ¦b - c¦, ¦c - d¦, ¦d - a¦, and go again. Greg considered the game in which a, b, c and d are real numbers. He described the asymptotic behavior of this game and of its higher dimensional analogues. In many instances the sequence converges to, and often arrives at, all zeroes. At Red River High School in Grand Forks, Greg is first in his class of 298. Involved in the math, science and Latin clubs, he has earned local, state, regional and national awards for his achievements. Greg was one of four American students who attended the 2006 International Chemistry Olympiad in South Korea, where he earned a silver medal. He enjoys Ultimate Frisbee, snowboarding, and is a black belt in Tae Kwon Do. The son of Dr. Ronald Brockman and Dr. Ellen Feldman, he plans to pursue a career at MIT or Harvey Mudd College as a math or physics researcher.