Question 107
Consider a figure consisting of 15 circles and 20 line segments as shown below. Each circle is labeled with a 0, 1, or 2, and we define the *beauty* of a labeling as the number of line segments whose endpoints are labeled with numbers that differ by 1.
Let $M$ be the largest possible beauty that can be achieved with any labeling. How many labelings exist that achieve the beauty of $M$?
Note that we distinguish labelings which can be obtained from each other by rotations or reflections.
Let $M$ be the largest possible beauty that can be achieved with any labeling. How many labelings exist that achieve the beauty of $M$?
Note that we distinguish labelings which can be obtained from each other by rotations or reflections.