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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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Solution We have a consensus Comment 6 of 6 |
Yes, 3 out of 7 is the best I could come up with also.

2 numbers, 2 blanks, 1 number, 2 blanks, repeat.

or, actually, any of 7 variations:
1100100
1001001
0010011
0100110
1001100
0011001
0110010.

I thought that I could slip an extra number in, taking advantage of the end conditions, but no dice.  Maximum elements in S is 300. 

  Posted by Steve Herman on 2014-01-02 15:25:05
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