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party but graph

Source: Indonesia IMO 2010 TST, Stage 1, Test 1, Problem 3

November 12, 2009
combinatorics proposedcombinatorics

Problem Statement

In a party, each person knew exactly 22 22 other persons. For each two persons X X and Y Y, if X X and Y Y knew each other, there is no other person who knew both of them, and if X X and Y Y did not know each other, there are exactly 6 6 persons who knew both of them. Assume that X X knew Y Y iff Y Y knew X X. How many people did attend the party? Yudi Satria, Jakarta