at a strange party, each person knew exactly 22 others
Source: 2010 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST)
October 3, 2020
combinatorics
Problem Statement
At a strange party, each person knew exactly others.
For any pair of people and who knew each other, there was no other person at the party that they both knew.
For any pair of people and who did not know one another, there were exactly 6 other people that they both knew.
How many people were at the party?