Always list divisors systematically. Avoid skipping 36 (a common mistake).

For coordinate geometry, the Shoelace Theorem (for area of polygons) and Pick's Theorem (for lattice points) are massive time-savers.

In this article, we’ll break down the format of the Sprint Round, walk through sample problems (similar in style and difficulty to actual nationals), and provide detailed solutions and strategies to help you excel.

Problem: In a rectangle $ABCD$, point $E$ is the midpoint of $AB$ and point $F$ is on $CD$ such that $DF = \frac13CD$. What fraction of the rectangle is shaded?

The sum of the interior angles of a triangle is always $180^\circ$.

Continue pattern: total valid triples after checking all k = .