For positive integers m,n≥2, let Sm,n={(i,j):i∈{1,2,…,m},j∈{1,2,…,n}} be a grid of mn lattice points on the coordinate plane. Determine all pairs (m,n) for which there exists a simple polygon P with vertices in Sm,n such that all points in Sm,n are on the boundary of P, all interior angles of P are either 90∘ or 270∘ and all side lengths of P are 1 or 3. gridcolouringpathsright anglecombinatoricsRMM Shortlist