Jigsaw puzzle on a Cartesian plane
Source: 2022 China TST, Test 3 P4
April 30, 2022
combinatoricsgeometrycombinatorial geometrylattice points
Problem Statement
Find all positive integer such that one can find a number of triangles in the Cartesian plane, the centroid of each triangle is a lattice point, the union of these triangles is a square of side length (the sides of the square are not necessarily parallel to the axis, the vertices of the square are not necessarily lattice points), and the intersection of any two triangles is an empty-set, a common point or a common edge.