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3

Part of 1999 Taiwan National Olympiad

Problems(1)

$1999$ people participating in an exhibition

Source: 8-th Taiwanese Mathematical Olympiad 1999

1/20/2007
There are 19991999 people participating in an exhibition. Among any 5050 people there are two who don't know each other. Prove that there are 4141 people, each of whom knows at most 19581958 people.
floor functioncombinatorics unsolvedcombinatorics