Suppose that
\(|a - b| + |b - c| + |c - d| + \dots + |m-n| + |n-o| + \cdots+ |x - y| + |y - z| + |z - a| = 20\)
What is the maximum possible value of \(|a-n|\)?
The inequality says that any two variables can differ by at most 20, so the maximum value is 20.
My guess is that the maximum will occur when all the variables (except for n) is zero.
This would mean that n = 10 and the maximum value of abs(a - n) = 10.
