2. Special cases
Clearly not possible in any of the above cases. Note in particular that the 3x3 case
leaves an odd square. This will obviously generalize to any case where n is odd.
3. Analogy - a Chessboard
The chessboard consists of a series of adjacent squares of opposite colours which can
originally be covered by the 2x1 rectangle shown. If when the two opposite squares are
removed the remaining figure can still be covered by the 2x1 rectangle then the two squares
temoved must have been of opposite colours. This contradicts the fact that they
are clearly the same colour. Thus it is impossible in the case of the chessboard - Eureka!
4. Have we solved the original problem? Clearly what is true for a chessboard is true for any square with an even number of smaller squares. Since we have already concluded that it is impossible to cover such a situation as the tho squares removed are she same colour, then the problem is solved. We cannot cover the remaining figure by non overlapping 2x1 rectangles.