Suppose that |a-b|+|b-c|+|c-a|=20. What is the maximum possible value of |a-b|?

Answer 1

|a-b| = 20 - |b-c|-|c-a|

If b>c and c>a
|a-b| = 20 - b + c - c + a =20+(a-b)
if a>b then a-b = 20 + a-b
and a-b = 0
if a < b then b-a = 20 -b+a
2b-2a = 20
|a-b| = 10
try others but I think you will find 10

Answer 2

ya that's right thats one of my AoPs questions and I had the same answer.