Question 144
Let $n\gt 1$ be an odd natural number. The fields of a $n \times n$ chessboard are colored alternately white and black, so that the four corner fields are black. An L-triomino is an L-shaped piece that covers exactly three squares of the board. For which values of $n$ is it possible to cover all black fields with L-triominoes so that no two L-triominoes overlap? For these values of $n$, determine the smallest possible number of L-triominoes that are necessary.