Junior Mathematical Olympiad, September 2019

Five smart students are sitting in a circle. The teacher gives one or more marbles to each of them. He explains that he has handed out a total of 18 marbles, and that everyone got a different number of marbles. Each student is allowed to see his own number of marbles, as well as the number of marbles of his neighbour on the left and his neighbour on the right.

Using only this information, each student must try to logically deduce the difference between the numbers of marbles of the two students opposite to him. The teacher has distributed the marbles in such a way as to minimise the number of students that are able to do this. How many students can do it? A) 0 B) 1 C) 2 D) 3 E) 5