There is a rectangular grid of $R$ rows and $C$ columns. $R \times C \bmod 4$ of the cells are painted black, and all other cells are white. In other words, there are at least 0 and at most 3 black cells, and the number of white cells is divisible by 4.
I want to cover the white cells using exactly $\lfloor \frac{R \times C}{4} \rfloor$ nonoverlapping tetrominoes. Assuming that the black cells do not divide the white cells into two or more disconnected regions, is it always possible for every possible position of black cells?
Note: I don't know the answer to this puzzle.