MathDB

On an

m\times n

grid there's a snail in each cell. Each round, the snail army can choose four snail and make them perform the complete Quadrilateral Dance, which is rotating the four snails clockwise by

90

degrees, moving each one to an adjacent cell. Find all pairs of positive integers

(m,n)

such that the snails can achieve any permutation by performing a finite number of times of Quadrilateral Dance.
Proposed by chengbilly

Problem Statement