Define a sequence by
For n a positive integer. Find
If you're having trouble solving the math problem above, take comfort in knowing you're hardly alone. At least two-thirds of the participants in the 32nd Annual Virginia Tech Regional Math Contest couldn't provide the answer either. In fact, two-thirds of the field scored a zero on the seven questions that made up the exam.
But that was not the case with the University of Rochester's Xiaoqing "Sean" Tang who scored 35 out of a possible 70 and tied for third.
Tang, a junior, is majoring in both mathematics and computer science. He says he was "pretty surprised to get such a high score."
"The basic motive for being involved in math competitions is the moment when you actually solve one problem," said Tang. "Trust me, you really get excited about that."
The competition was held on Saturday, October 30. The contestants, who represented 97 schools from 26 states, took the two-and-one-half hour supervised exam on their own campuses. The results were released last week, and Steven Gonek, chairman of the University's math department, was "delighted."
"We put a lot of effort into developing the undergraduate curriculum and providing a good atmosphere," said Gonek. "And competitions are one part of it."
Two other students from the University of Rochester, senior Christopher Kauffman and junior Kevin Lin, each scored 20 points, earning them a tie for 17th place. That score put them in the top three percent of the field.
Dan Geba, associate professor of mathematics, prepared the Rochester students for the competition and served as their coach. He considered this year's Virginia Tech contest more difficult than usual, based on the fact that no one came close to a perfect 70 and more than 60% scored zero.
Geba attributes the success of this year's team to several factors. He instituted a weekly problem-solving seminar four years ago to train students in strategies and techniques. It's also important, he said, that the math department offers very competitive courses.
The department's attention now turns to the William Lowell Putnam Mathematical Competition—the country's number one math contest—to be held this year on Saturday, December 4. Tang, Kauffman and Lin will all be on the University of Rochester team.
Tang was part of the University of Rochester computer science team that dethroned MIT in last year's regional finals of the Association of Computing Machinery's annual competition, which has been dubbed the "Battle of the Brains."