2009 integers around a circle
Source: 2009 Argentina OMA Finals L3 p5
January 15, 2023
combinatorics
Problem Statement
Around a circle are written integers, not necessarily distinct, so that if two numbers are neighbors their difference is or . We will say that a number is huge if it is greater than its two neighbors, and that it is tiny if it is less than its two neighbors. The sum of all the huge numbers is equal to the sum of all the tiny numbers plus . . Determine how many odd numbers there can be around the circumference.