Cases n=3,4,5 fail because a friendship graph that is an n-gon fails with friendship # = 2 for all nodes.
1/
If the node with highest Friendship # has Friendship # >= 3 then that immediately either defines a triad of mutual friendship or a triad of mutual strangers from the first three friend nodes.
Therefore Friendship # <= 2 for all nodes.
2/
3/
If the friendship is 2 chains then two ends of the longest chain (or either if both 3 long) and any node from the other is a stranger-triad.
Therefore the answer is n = 6.
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