Problem

Source: Tuymaada Junior 2003 p6

Tags: combinatorics, Sum, circle



On a circle, numbers from $1$ to $100$ are arranged in some order. We call a pair of numbers good if these two numbers do not stand side by side, and at least on one of the two arcs into which they break a circle, all the numbers are less than each of them. What can be the total number of good pairs?