Question 7
Given a regular 103-sided polygon with 79 vertices are colored red and the remaining vertices are colored blue. Denote $A$ to be the number of pairs of adjacent red vertices and $B$ to be the number of pairs of adjacent blue vertices.
a) Find all possible values of $(A, B)$.
b) Determine the number of pairwise non-similar colorings of the polygon satisfying $B = 14$. Note that two ways of colorings are considered similar if one of them can be obtained from another with a rotation at the circumcircle of the polygon.
a) Find all possible values of $(A, B)$.
b) Determine the number of pairwise non-similar colorings of the polygon satisfying $B = 14$. Note that two ways of colorings are considered similar if one of them can be obtained from another with a rotation at the circumcircle of the polygon.