A function F is such that this relationship holds for all real x.

F(x) = F(398-x) = F(2158-x) = F(3214-x)

What is the maximum number of distinct values that can appear in the list F(0), F(1), F(2), ..., F(999).

**Do I miss something?**

1-398 - only 199 distinct values possible due to F(x) = F(398-x).

399-999 601 more values possible,

**total 800..**

**Who cares about **F(x) = F(2158-x) = F(3214-x)?? (*)

**That is the maximum possible.**

If we were asked to provide a function F(x) or to prove that such function with the restrictions (*) exists, that would be another story.

*Edited on ***September 16, 2014, 7:06 am**