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?

Question

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?

Answer 1

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.