Please answer ASAP and I will upvote right away for the correct answer with work shown:

There are 6 balls A, B, C, D, E, and F laid out in front of you in that order. Each ball has a number between 1 and 6 on it. (The numbers are mutually independent). A ball is an "averager" if its number is the exact average ofthe numbers on the left and right of itself. For example, B is an averager in the following situations: \"A=1, B=3, C=5\