Israel 2011 Q3 - Uniform triplets of ministers
Source: Israel National Olympiad 2011 Q3
August 8, 2019
combinatoricscountinggraph theory
Problem Statement
In some foreign country's government, there are 12 ministers. Each minister has 5 friends and 6 enemies in the government (friendship/enemyship is a symmetric relation). A triplet of ministers is called uniform if all three of them are friends with each other, or all three of them are enemies. How many uniform triplets are there?