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$.
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$.