Question 3
A regular polygon has $103$ vertices. Color $79$ vertices red and all remaining vertices blue. Let $A$ be the number of adjacent red-red pairs and $B$ the number of adjacent blue-blue pairs.
(a) Find all possible pairs $(A,B)$.
(b) Find the number of colorings for which $B=14$, where two colorings are identified if one is obtained from the other by a rotation about the circumcenter.
(a) Find all possible pairs $(A,B)$.
(b) Find the number of colorings for which $B=14$, where two colorings are identified if one is obtained from the other by a rotation about the circumcenter.