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Supreme Subset (Posted on 2014-01-02) Difficulty: 3 of 5
Let us define the set T = {1,2,3,...,700}. Now, S is a subset of T such that no two numbers in S differ by a difference of 2 or 5.

Determine the largest number of elements that S can have.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: possible solution | Comment 2 of 6 |
(In reply to possible solution by Ady TZIDON)

That doesn't work.  9 and 11 differ by 2.

I doubt that 350 is achievable.  Any time two numbers in S are consecutive, the next two need to be absent from S, and this is without even considering differences of 5.

Have to work now, so can't figure it out.

Edited on January 2, 2014, 2:27 pm
  Posted by Steve Herman on 2014-01-02 13:00:00

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