Question 89
Let it be $n \geq 4$. Let's number $n$ points on the circle with numbers from 1 to $n$. Non-adjacent points numbered with $a$ and $b$ are said to be a regular pair if, at least on one of the arcs defined by $a$ and $b$, all points are numbered with numbers smaller than $a$ and $b$. Prove that the number of correct pairs is equal to $n-3$.