Find the pair


Suppose that in a certain society, each pair of persons can be classified as either amicable or hostile. We shall say that each member of an amicable pair is a friend of the other, and each member of a hostile pair is a foe of the other. Suppose that the society has f3fe67cd85ba57a3c30adc14b0b68a259e69d403 persons and 252bd9794edd4df96b45c8d9d775440a737db9c0 amicable pairs, and that for every set of three persons, at least one pair is hostile. Prove that there is at least one member of the society whose foes include 123271d6b63afbce30018715324abf325d4671aa or fewer amicable pairs

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