6

Part of 2003 Junior Tuymaada Olympiad

Problems(1)

1-100 numbers on a circle, pair of good numbers include only smaller

Source: Tuymaada Junior 2003 p6

On a circle, numbers from

1

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?

combinatoricsSumcircle