You live on an island where there are only two kinds of people: the ones who always tell the truth (truth tellers) and those who always lie (liars). You are accused of crime and brought before the court, where you are allowed to speak only one sentence in your defense. What do you say in each of the following situations?
1. If you were a liar (the court does not know that) and you were innocent. And it is an established fact that a liar committed the crime.
2. Same situation as above, but you are the one who committed the crime.
3. If you were a truth teller (the court does not know that) and you were innocent. And it is an established fact that a truth teller committed the crime.
4. If you were innocent and it is an established fact that the crime was not committed by a “normal” person. Normal people are that new immigrant group who sometimes lie and sometimes speak the truth. What sentence, no matter whether you were a truth teller, liar, or normal, can prove your innocence?
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