numbers 1 - 300 around a circle
Source: 2019 Argentina OMA Finals L3 p6
January 16, 2023
combinatorics
Problem Statement
The natural numbers from up to are evenly located around a circle. We say that such an ordering is alternate [/i ]if each number is less than its two neighbors or is greater than its two neighbors. We will call a pair of neighboring numbers a good pair if, by removing that pair from the circumference, the remaining numbers form an alternate ordering. Determine the least possible number of good pairs in which there can be an alternate ordering of the numbers from at inclusive.