3

Part of 1995 Taiwan National Olympiad

Problems(1)

$n$ persons meet in a meeting

Source: 4-th Taiwanese Mathematical Olympiad 1995

n

persons meet in a meeting, and that each of the persons is acquainted to exactly

8

others. Any two acquainted persons have exactly

4

common acquaintances, and any two non-acquainted persons have exactly

2

common acquaintances. Find all possible values of

n

combinatorics proposedcombinatorics