Can the number of people be 65?
Source: Vietnam TST 1996 for the 37th IMO, problem 5
June 26, 2005
parameterizationlinear algebramatrixcombinatorics unsolvedcombinatorics
Problem Statement
There are some people in a meeting; each doesn't know at least 56 others, and for any pair, there exist a third one who knows both of them. Can the number of people be 65?