12th Eötvös Competition Problems 1905

1.  For what positive integers m, n can we find positive integers a, b, c such that a + mb = n and a + b = mc. Show that there is at most one such solution for each m, n. 2.  Divide the unit square into 9 equal squares (forming a 3 x 3 array) and color the central square red. Now subdivide each of the 8 uncolored squares into 9 equal squares and color each