Question 24
In 3009, King Warren of Australia suspects the Earls of Akaroa, Bairnsdale, Claremont, Darlinghurst, Erina and Frankston are plotting a conspiracy against him. He questions each in private and they tell him:
Akaroa: Frankston is loyal but Erina is a traitor.
Bairnsdale: Akaroa is loyal.
Claremont: Frankston is loyal but Bairnsdale is a traitor.
Darlinghurst: Claremont is loyal but Bairnsdale is a traitor.
Erina: Darlinghurst is a traitor.
Frankston: Akaroa is loyal.
Each traitor knows who the other traitors are, but will always give false information, accusing loyalists of being traitors and vice versa. Each loyalist tells the truth as he knows it, so his information on traitors can be trusted, but he may be wrong about those he claims to be loyal.
How many traitors are there?
Akaroa: Frankston is loyal but Erina is a traitor.
Bairnsdale: Akaroa is loyal.
Claremont: Frankston is loyal but Bairnsdale is a traitor.
Darlinghurst: Claremont is loyal but Bairnsdale is a traitor.
Erina: Darlinghurst is a traitor.
Frankston: Akaroa is loyal.
Each traitor knows who the other traitors are, but will always give false information, accusing loyalists of being traitors and vice versa. Each loyalist tells the truth as he knows it, so his information on traitors can be trusted, but he may be wrong about those he claims to be loyal.
How many traitors are there?