TUYMAADA 2009 S6

An arrangement of chips in the squares of $n\times n$ table is called sparse if every $2\times 2$ square contains at most 3 chips. Serge put chips in some squares of the table (one in a square) and obtained a sparse arrangement. He noted however that if any chip is moved to any free square then the arrangement is no more sparce. For what $n$ is this possible?

Proposed by S. Berlov