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“Twenty-one girls and twenty-one boys took part in a mathematical competition. It turned out that (a) each contestant solved at most six problems, and (b) for each pair of a girl and a boy, there was at least one problem that was solved by both the girl and the boy. Prove that there was a problem that was solved by at least three girls and at least three boys.”
Or give up immediately and leave the problem-solving to the high-school-aged experts of the U.S. International Mathematical Olympiad team—which is exactly what author and freelance journalist Steve Olson did for his latest book, Count Down: Six Kids Vie for Glory at the World’s Toughest Math Competition.
“[You can do] these wonderful things with the basics [of mathematics],” says the 47-year-old Bethesda resident. “I see these kids as artists.”
Olson, who graduated from high school in 1974, the same year the United States fielded its first Olympiad team, has been intrigued by the competition ever since he was a teen with promising math aptitude. After it was announced that the Washington area would host the annual event in 2001, Olson seized the opportunity. He attended a weekslong training camp for Olympiad contestants held at Georgetown University, spent some time with the six kids who would become his book’s subjects, and even got to try his hand at the complicated problems they were drilling.
“When they handed out the problem sets, I would grab them,” recalls Olson, “and I couldn’t get anywhere.”
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At the subsequent Olympiad, Olson watched as 473 teens culled from the best math students in 83 countries were each given packets containing three problems that had to be solved in four-and-a-half hours. Granola bars and bathroom breaks were provided, with the latter chaperoned to prevent foul play. And when the first round was over, the kids got to do it all again the next day. “It’s as much a mind game as it is an endurance contest,” says Olson.
As is his book: Olson structured Count Down around the very problems that appeared at the 2001 Olympiad. The book’s breakout star is 18-year-old Reid Barton of Arlington, Mass., who that year wrapped up the most legendary run in Olympiad history: gold medals in four straight competitions. Though a purist teammate teased him about it, Barton managed the win—and a perfect score on all six problems—by, among other methodologies, “using the Axiom of Choice 441 times.”
If you don’t know that particular procedure, don’t blame yourself. “We have a terrible attitude [in the United States],” says Olson. “It’s socially acceptable to say that you’re no good in math and don’t like it.” He suggests that Americans’ skills could be improved through an Olympiad-style approach to teaching: make math students sink or swim.
“In Japanese classrooms,” he writes in Count Down, “teachers want their students to struggle with problems, because they believe that’s how students come to really understand mathematical concepts.”
That, in fact, is the concept behind the problem about the 42 kids at a mathematical competition. The third and most difficult in the 2001 Olympiad’ first-round packet, it’s what’s known as an “all or nothing problem”—meaning that the judges expect each of the contestants to score either a perfect 7 or a 0.
“‘It’s a problem that could be understood by any student,’” one judge explained to Olson. “‘But to solve it, that’s another story.’ ” —Mike Kanin