2002 IMO Shortlist S16

For $n$ an odd positive integer, the unit squares of an $n\times n$ chessboard are coloured alternately black and white, with the four corners coloured black. A it tromino is an $L$ -shape formed by three connected unit squares. For which values of $n$ is it possible to cover all the black squares with non-overlapping trominos? When it is possible, what is the minimum number of trominos needed?

对于$n$奇数正整数，$n\times n$棋盘的单位方格颜色交替为黑色和白色，四个角为黑色。 it tromino 是由三个相连的单位方块形成的 $L$ 形状。对于哪些 $n$ 值，可以用不重叠的特罗米诺覆盖所有黑色方块？如果可能的话，最少需要多少个特罗米诺骨牌？