The centre of a circle is the origin of N vectors whose ends divide the circle in N equal arcs . Some of the vectors are blue and some are red . We calculate the sum of the angles formed between each pair consisting of a red vector and a blue vector (the angle being measured anticlockwise from red to blue) and divide this sum by the total number of such angles . Prove that the "mean angle" thus obtained is 180o. (V. P roizvolov) combinatoricscombinatorial geometry