Anna, Ben and Chris sit at the round table passing and eating nuts. At first only Anna has the nuts that she divides equally between Ben and Chris, eating a leftover (if there is any). Then Ben does the same with his pile. Then Chris does the same with his pile. The process repeats itself: each of the children divides his/her pile of nuts equally between his/her neighbours eating the leftovers if there are any. Initially, the number of nuts is large enough (more than 3). Prove that a) at least one nut is eaten; (3 points) b) all nuts cannot be eaten. (3 points)