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Distinct Value Deduction (Posted on 2014-09-14) Difficulty: 3 of 5
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).

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Question Do I miss something? | Comment 1 of 7
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
  Posted by Ady TZIDON on 2014-09-15 05:58:04

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