Question 154
At the Scuola Normale, this year's freshmen in the Science class are of four types: Mathematicians, Physicists, Chemists and Biologists. In the canteen they all find themselves seated together around a round table; each of them has exactly one person seated opposite them, and moreover, for every student, the set consisting of the student, their right neighbour, their left neighbour and the student seated opposite contains all four types of students. How many can the freshmen of the Science class be, suitably divided among the four types, knowing that they are between $30$ and $50$ (inclusive)? Give as the result the sum of all possible answers.
(A) 40
(B) 80
(C) 120
(D) 200
(E) 440
(A) 40
(B) 80
(C) 120
(D) 200
(E) 440