Explaining the IMPOSSIBLE Tetromino Problem

Is it possible to cover an n by n grid with T-shaped tetrominos so that none overlap orhang over the edge? This problem comes from the Canada Junior Mathematical Olympiad.

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[pandorairq]

Its actually not true that the amount of white squares on a chess board is equal to the number of black squares. For any uneven number one is bigger (by exactly 1).
Example n=1: trivial

N=3
BWB
WBW
BWB
#B = 5
#W = 4

[Vampire-Catgirl]

I feel like you should specify if you only mean the T shaped piece