Thirty numbers are arranged on a circle in such a way that each number equals the absolute difference of its two neighbors. Given that the sum of the numbers is $2000$, determine the numbers.
Source: Moldova 2000 Grade 8 P2
Tags: number theory, algebra
Thirty numbers are arranged on a circle in such a way that each number equals the absolute difference of its two neighbors. Given that the sum of the numbers is $2000$, determine the numbers.