Posted by **bravo** on Monday, April 29, 2013 at 12:04pm.

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!!!! -
**Steve**, Monday, April 29, 2013 at 2:57pm
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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