Four students competing for the first time were the winners in the 2016 Northern Illinois University Mathematics Contest, held March 2.

Rebecca Dziubla, a junior **mathematical sciences** major from Roselle, took the $100 first prize. Heidi Zipoy, a junior mathematical sciences major from Elgin, won the second-place $75 prize.

Jordan Rucinski, a junior mathematical sciences major from Esmond, and Gregory Solomon, a sophomore **mechanical engineering** major from Bartlett, tied for third place, which came with a $50 prize for each.

The winners will be recognized Sunday, April 17, at the Department of Mathematical Sciences’ Awards Ceremony and Reception.

Open to all full-time undergraduates, the annual NIU 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.

Each contestant turns in solutions to six problems. Topics this year ranged from logic puzzles, algebra and geometry to calculus and linear algebra.

Professors **Harvey Blau**, **Y. C. Kwong**, **Deepak Naidu** and **Gleb Sirotkin** supervised the competition.

In case you’re wondering about the difficulty of the contest problems, the following logic brainteaser was a popular choice among the contestants:

Arlo, Bruno, and Carlo took their girlfriends to a dance. At one time, Elsa was dancing with Arlo, Dakota was dancing with Fiona’s boyfriend, Bruno was dancing with Carlo’s girlfriend, and Carlo was dancing with Arlo’s girlfriend. Find who was dancing with whom and match up each girlfriend and boyfriend. Explain your answer.

And here is a problem that combined calculus and geometry:

Let f(t) and g(t) be differentiable functions such that (derivatives) f'(t) = 2g(t) and g'(t) = -3f(t) for all real numbers t. Show that for all t, the points (f(t), g(t)) lie on an ellipse.

For more information, email blau@math.niu.edu.