There is a square board made of at least 4 equal-sized squares. The number of squares in the board is a power of 2. An unlimited number of L-shaped triominoes are given. Each triomino is made of 3 equal-sized squares. Each equal-sized square that makes a triomino has the same dimensions as that of each equal-sized square that makes the square board.
The square board needs to be tiled with the L-shaped triominoes such that each square is covered at most once without parts of each triomino extending beyond the 3 squares it covers.
What is the minimum number of squares that can't be covered with the triominoes?