A tromino is a $3 \times 1$ block:

What sized rectangles may be made using trominoes? You can print off and cut out trominoes from this sheet . Alternatively, if you have a set of the game Jenga, then use the blocks as trominoes (but check they are $3 \times 1$ first)

Can you cover $63$ squares of an $8\times 8$ chessboard using trominoes? (Why can't you cover $64$?). If so, which square remains uncovered, and are there other arrangements of the trominoes which would lead to a different square being left uncovered?

Think of some other squares which cannot be covered with trominoes. Can you "almost" cover them, leaving only one hole? When can an $n \times n$ square be covered or "almost" covered?