Problem 16 (number theory): The number of ways to write any positive integer $N$ as a sum of positive consecutive integers is the number of odd divisors of $N$.
Problem 17 (angle bisectors): Angle bisectors can and often apply to more than just one triangle.
Problem 18 (graphing): When having to graph an equation, sometimes it is helpful to do casework. Often times there will be symmetry; for instance with absolute values with $x$ or $y$ values, there will be symmetry across the x-axis or y-axis
Problem 20 (counting): For many counting problems that include graphical forms, there will only be a few cases that we are looking for. In this problem, we are only looking for two cases (which simplifies the problem):
Problem 23 (3D geometry): The equation $\lvert x \rvert + \lvert y \rvert + \lvert z \rvert \leq 1$ forms an octahedron.
Problem 24 (gcd/lcm): With GCD restrictions, sometimes they can be ignored for the time being and then reconsidered once calculations are done. For example, with this problem, the initial GCD requirement can be ignored and first, since then all that’s needed is for the final answer to be multiplied by $77$.