Problem 10 (2 x 3 graph theory): Problems rarely make you just brute force everything out. Analyze the situation, come up with anything you can think of that makes progress.
Problem 15 (Finding area): Consider your options. Don’t be set on one method or idea for a problem.
Problem 17 (Complex numbers): Points $a$, $b$, and $c$ on the complex plane form an equilateral triangle if and only if $a^2 + b^2 + c^2 = ab + bc + ca$.
Problem 22 (Estimation): Start with finding what you can and then working from there. Many problems require multiple insights to be solved and aren’t completed with just one or two simple steps.
Problem 24 (Complex numbers): $-\frac{1}{2} \pm \frac{\sqrt{3}}{2} i$ are solutions to $x^3 = 1$.
Problem 25 (Centroids): Vectors are commonly used in problems regarding centroids.