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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 \(|a-n|\)?

 Mar 13, 2020
 #1
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The inequality says that any two variables can differ by at most 20, so the maximum value is 20.

 Mar 13, 2020
 #2
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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.

 Mar 14, 2020

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