MathDB

For positive integers

m,n \geq 2

, let

S_{m,n} = \{(i,j): i \in \{1,2,\ldots,m\}, j\in \{1,2,\ldots,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

S_{m,n}

such that all points in

S_{m,n}

are on the boundary of

P

, all interior angles of

P

are either

90^{\circ}

270^{\circ}

and all side lengths of

P

are

1

3

Problem Statement