“Ten women sit in 10 seats in a line. All of the 10 get up and then re-seat themselves using all 10 seats, each sitting in the seat she was in before or a seat next to the one she occupied before. In how many ways can the women be reseated?”
The ability of some high school students to solve such problems within less than a minute fascinates peers and teachers alike. Yet many mathletes believe they are not “special” compared to the average student.
Senior math club member Evan Ye thinks that practice, rather than an innate ability in math, makes a mathlete.
“Some people tend to grasp math concepts faster, and that may be because of early exposure or whatnot, but at the end I still think it is the practice that makes the most difference,” Ye said.
Exposed to extra math programs in elementary school, sophomore math club officer Priyanka Krishnamurthi also reasons that practice and an early exposure to the subject has helped her develop her strength in math.
“I enjoyed math from a very young age,” Krishnamurthi said. “My parents also encouraged me to do math by putting me in programs, and I really started enjoying it.”
However, according to alumnus Amol Aggarwal, who now attends MIT, developing a strong liking for math at an early age is not crucial to becoming an eventual mathlete.
“When I was young, I did not like [math] too much,” Aggarwal said. “However, as I began to learn more about math, I started to like it more.”
Math club adviser P.J. Yim also stresses the importance of at least giving math a try.
“I think the initial success, and seed of success, creates the desire,” Yim said. “There’s somebody to say, ‘Wow! You did a great job!’ Sometimes that’s a great motivator.”
Yim recognizes the excitement that mathletes feel for the subject as another crucial ingredient to their success by providing the motivation students need to solve challenging problems.
“It is so challenging, and they find it very invigorating,” Yim said. “They just do it because they love to do it.”
The students particularly find it fulfilling to successfully solve a math problem.
“It’s the action of taking a problem and finishing it to the end,” Ye said. “A lot of satisfaction comes from that, and that is what I like about it the most.”
A common method mathletes use to solve complex problems is pattern recognition.
“I think it is very intuitive. When I am actually doing a problem, it’s more of an automatic feeling,” Ye said. “But if nothing comes to mind, I try to cut [the problem] in such a way that I can recognize patterns.”
According to Ye, pattern recognition involves identifying the individual steps of a problem.
“Let’s say you’re assigned a large project that seems impossible. What you do is you break it into smaller pieces, each of which you know how to do,” Ye said. “That’s like pattern recognition; you break a tricky math problem into problems you already know how to solve.”
Aggarwal also finds fascinating the ways in which a complex problem can be broken down into simpler terms.
“It is interesting to see how simpler facts can be linked together to form solutions to more complicated questions,” Aggarwal said. “One way for people to start a problems is by trying specific examples and small cases of a more general question.”
According to Krishnamurthi, the most important factor needed to become a mathlete is motivation.
“You cannot push someone to like math unless they have an inclination for it,” Krishnamurthi said. “A person has to have some sort of drive towards math, whether it was something that was brought upon them or something that they truly enjoy.”
Yim also sees the value of having a drive for math because he acknowledges that without it, a student would not be able to or want to solve challenging math problems.
“There’s a lot of hard work involved,” Yim said. “For them to tackle something so difficult and be driven, I think it really takes special people to do that.”
Not only do mathletes have to be accurate while solving math problems during competitions, but they also have to be fast. Although Ye and Krishnamurthi believe that such a skill can be attained through practice, Yim thinks otherwise. According to him, the top mathletes are “naturally gifted.”
Through practice, however, Ye has learned how to think outside the box, which has, according to him, helped him in math competitions. Math has taught Ye other useful skills as well.
“Math has taught me to keep a broad outlook and question things that go on and find what the best way of approaching it is,” Ye said.