There is a rectangle of size $9\times 11$. Is it possible to divide it using 1 tromino and $N$ tetrominoes?
I have tried a lot and it seems that this is not possible, thus I want to prove it is not possible.
- Such a simple method as counting the number of squares, count add/even contradictions - seems to not work.
- Coloring method. Maybe this works, but then we have not found the right coloring.
What I mean - I read that sometimes such problems can be proved by coloring rectangle squares using some specific pattern and this could give some contradiction usually with something odd/even.
We tried a lot of coloring patterns (the simplest one was coloring rectangle squares black and white as chessboard, also coloring first line black, second one line white etc., also tried other coloring patterns). We have not found any contradictions that help us to prove that this is not possible.
It would be nice if someone suggests any ideas, how to proceed with such type of problems.
P.S. I tried this to solve together with my 5th grader and now I am so much into it that I really want to solve it