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Let A be a subset of T={1,2,…,100} subject to the condition that if 2 distinct elements a and b are in A, then a+b is not in A. What is the maximum value of |A|, which is the number of elements in A?

  • geometry!!!! -

    Looks like 51 to me.
    If 49 is in A, 50,51 cannot be in A
    If 48 is in A, 50,51,52 cannot be in A.
    if n<50 is in A, we must exclude 51-n elements from A.

    So, including 50,51,...100 in A, we get 51 elements.

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