  We prove that the entropy compression method systematized by L. Esperet and
A. Parreau can be applied to any problem formulated in the variable version of
the Lovasz Local Lemma. As an application, we prove the existence of legitimate
colorings for projective planes with small orders, which extends results of N.
Alon and Z. Fured. In fact, we allow different numbers of colors, proving that
projective planes of any order can be legitimate colored with 42 colors.
