SE-SKOLORNAS 2010 Problem 6

An infinite number of squares on an infinitely square grid paper are painted red. Show that you can draw a number of squares on the paper, with sides along the grid lines, such that:

(1) no square in the grid belongs to more than one square (an edge, on the other hand, may belong to more than one square)

(2) each red square is located in one of the squares and the number of red squares in such square is at least $1/5$ and at most $4/5$ of the number of squares in the square.

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PS. I always post the original wording when I doubt about my (using Google) translation.