Hi, I'm new to this forum and it's been frankly over 2 decades since I graduated from university... so I'm pretty rusty and hoping to get a little help with a certain math problem that has popped into my work life. I'd be forever grateful for any advice in solving this one that I've been wracking my old brain with for the past couple hours but getting nowhere.

Basically I'm trying to normalize a value, and in order to do that I need to know the maximum value it can have. I have two summations that both are equal to 1:

(n is a constant to all)

(o[1] + ... + o[n]) = 1

(c[1] + ... + c[n]) = 1

and I am taking the difference of each variable and summing their absolute values:

|o[1] - c[1]| + ... + |o[n] - c[n]|

Does anyone know what the maximum value that thing above can have?

Jeremy