As x ranges over all real values, what is the minimum value of f(x)=|x-123|+|x-456| + |x-789|

Answer 1

Note that |x-a|+|x-b| is constant (b-a) for a<=x<=b

So, since |x-123|+|x-789| is constant for 123<=x<=789, the minimum occurs at x=456, and is 666.

devilishly clever!

Answer 2

Strange r meets stranger