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a) Suppose that \[|a - b| + |b - c| + |c - a| = 20.\] What is the maximum possible value of $|a - b|$?

b) 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 $|a - n|$?

Guest Apr 24, 2018

#1**+1 **

Here's the first one

Let a > c > b

And since a > b, then l a - b l = a - b

And since c > b, the l b - c l = c - b

And since a > c, then l c - a l = a - c

Then we have that

(a - b) + ( c - b) + ( a - c) = 20 simplify

2a - 2b = 20 divide through by 2

a - b = 10

And this is the max value for l a - b l

CPhill Apr 24, 2018