From the home page of Duke University Math Meet:
"Duke Math Meet (DMM) is a regional mathematics competition for high school students held at Duke University every year. The contest is organized by the members of the Duke University Mathematics Union (DUMU), and is sponsored by the mathematics department. The DMM lasts for one day from morning to afternoon, during which the students have fun solving challenging mathematics problems, while making many new friends with contestants from other schools and states."
Here are some of the past papers