I have shown the pairs that can form the sum of 11.
Now, consider example. Lets say that I select 1,2,3,4,5. Now, I select 2 more elements. These 2 elements will form pairs with atleast 2 elements from first 5 elements selected previously. Hence, there are atleast 2 pairs that sum up to 11.
Hence, the statement proved.(You can try out any 5 elements at first place. Next 2 elements will definitely map to 2 elements selected previously).
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