Question 88
You are responsible for arranging a banquet for an agency. In the agency, some pairs of agents are enemies. A group of agents are called *avengers*, if and only if the number of agents in the group is odd and at least 3, and it is possible to arrange all of them around a round table so that every two neighbors are enemies.
You figure out a way to assign all agents to 11 tables so that any two agents on the same tables are not enemies, and that's the minimum number of tables you can get. Prove that there are at least $2^{10} - 11$ avengers in the agency.
You figure out a way to assign all agents to 11 tables so that any two agents on the same tables are not enemies, and that's the minimum number of tables you can get. Prove that there are at least $2^{10} - 11$ avengers in the agency.