We have a $m*n$ rectangle prove that it can't filled with these tetrominos.
tetrominos used:$L$_tetromino-straight tetromino-$T$_tetromino-square tetromino-skew tetromino.
My attempt:Because all of our shapes that we want to fill with are tetrominos then our rectangle can't filled if $m*n$ is not a multiply of $4$.After that I tried different kinds of coloring to show it can't be filled the resault can easily proved if we should use every kind of tetrominos but it is impossible for me to prove it can't filled if we can use just $1$ kind or so tetrominos.Please suggest me a kind of coloring that I can prove this.Thanks.