The 26th running of the annual event was held March 23. The winners were recognized Sunday, April 17, at the Department of Mathematical Sciences’ Awards Ceremony and Reception.
Chi Zhang, a senior computer science/mathematical sciences major from Qingdao, China, won first place for the third year in a row, and was awarded the first prize of $100. Xiaoyang Bi, a senior mathematical sciences (actuarial science) major from Vernon Hills, took the second prize of $75. Taylor Brysiewicz, a freshman mathematical sciences major from Bartlett, finished third and received $50.
The annual Northern Illinois University Mathematics Contest has a format where freshmen and sophomores have a fair chance to compete with juniors and seniors. The underclassmen have fewer restrictions on their choice of problems to attempt.
The contest is open to all full-time undergraduates at NIU. Each contestant turns in solutions to a choice of six out of 11 problems. Topics this year ranged from high school-level algebra, geometry and elementary number theory through calculus, linear algebra and differential equations.
Here is the easiest problem from this year’s contest: It is spring, and there are 12 hours of daylight. A caterpillar climbs a vertical wall at a speed of 1 foot per hour during the day, and then sleeps for 12 hours of darkness, during which it slides downward at ½ foot per hour. The wall is 48 feet high. How long will it take the caterpillar to reach the top of the wall?
A more difficult problem, although it only involves knowledge of matrix multiplication from linear algebra, was the following: Does there exist a 3-by-3 matrix with four positive entries and five zero entries that has some power with all positive entries? Prove your answer.