# Be real!

Consider all sets of 100 real numbers $$r_i$$ whose sum is positive.

Define $$t_{ij} = r_i + r_j$$ for $$i < j$$. There are $${ 100 \choose 2 } = 4950$$ such pairs.

What is the maximum number of $$t_{ij}$$ which are non-positive?

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