CGMO 2006 Problem 4

$8$ people participate in a party.

(1) Among any $5$ people there are $3$ who pairwise know each other. Prove that there are $4$ people who paiwise know each other.

(2) If Among any $6$ people there are $3$ who pairwise know each other, then can we find $4$ people who pairwise know each other?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.