MathDB

A rectangle of size

m \times n

has been filled completely by trominoes (a tromino is an L-shape consisting of 3 unit squares). There are four ways to place a tromino 1st way: let the "corner" of the L be on top left 2nd way: let the "corner" of the L be on top right 3rd way: let the "corner" of the L be on bottom left 4th way: let the "corner" of the L be on bottom right Prove that the difference between the number of trominoes placed in the 1st and the 4th way is divisible by

3

Problem Statement