Imagine an island inhabited by trolls. These trolls were from either one of two clans. These clans were The Truthfuls (could only tell the truth) and the Liars (only spoke in lies). One day I met three trolls. I asked them what clan they were all from. The first one responded "All of us are Liars". The second one said "No, only two of us are Liars". Then the third one said "That's not true either. Only one of us is a Liar". Which clan is each troll from?