perplexus.info :: Just Math : Distinct Value Deduction

Distinct Value Deduction (Posted on 2014-09-14)

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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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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