natural numbers from 1 to 100 are arranged on a circle
Source: Russian Olympiad 2004, problem 9.7
May 3, 2004
combinatorics unsolvedcombinatorics
Problem Statement
The natural numbers from 1 to 100 are arranged on a circle with the characteristic that each number is either larger as their two neighbours or smaller than their two neighbours. A pair of neighbouring numbers is called "good", if you cancel such a pair, the above property remains still valid. What is the smallest possible number of good pairs?