Legitimate colorings of projective planes

For a projective plane _n of ordern, let(_n) denote the minimum numberk, so that there is a coloring of the points of _n ink colors such that no two distinct lines contain precisely the same number of points of each color. Answering a question of A. Rosa, we show that for all sufficiently largen, 5 (_n) 8 for every projective plane _n of ordern.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation