2017 Guts #30: Polygon with vertices on grid
Source:
February 21, 2017
combinatorics
Problem Statement
Consider an equilateral triangular grid with points on a side, where each row consists of points spaced unit apart. More specifically, there is a single point in the first row, two points in the second row, ..., and points in the last row, for a total of points. Let be a closed non-self-intersecting polygon which has vertices, using each point in exactly once. Find the sum of all possible values of the area of .