Sheldon, Leonard and Wolowitz play a sizzling game of rock-paper-scissors for three players. In every round, each player simultaneously shows one of the three shapes. Rock beats scissors, scissors beats paper, and paper beats rock. If in a round exactly two distinct shapes are shown then 1 point is added to the score of the one player or to the two players who showed the winning shape, otherwise no point is added.
After many rounds of playing it occurred that each of the shapes had been shown exactly the same number of times. Is it possible that at this moment the total sum of points of Sheldon and Leonard and Howard was 2015?