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First one:

 

Suppose that \(|a - b| + |b - c| + |c - a| = 20.\)

What is the maximum possible value of \(|a - b|\)?

 

Second one:

 

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 \(|a-n|\)?

 Apr 19, 2020
 #1
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By the triangle inequality, any two variables differ by at most 20.  So the maximum value of |a - b| is 20, and the maximum value of |a - n| is 20.

 Apr 19, 2020

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