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.

Write down the numbers and starting at 1 consider if each number can be kept or discarded you get the sequence of remaining numbers:
1,2,5, 8,9,12, 15,16,19
which is a cycle of length 7 of which 3 remain.
3/7 or 700 = 300

I don't know if this can be improved.

Posted by Jer on 2014-01-02 15:04:41