Suppose that on an island there are three types of people: knights, knaves and n

Question

Suppose that on an island there are three types of people: knights, knaves and normal's. Knights always tell the truth, knaves always lie, and normal's sometimes lie and sometimes tell the truth. Detectives questioned three inhabitants of the island - Amy, Brenda and Claire - as part of the investigation of a crime. The detectives knew that one of the three committed the crime, but not which one. They also knew that the criminal was a knight, and that the other two were not. Additionally, the detective recorded their statements: Amy: "I am innocent". Brenda: "What Amy says is true". Claire: "Brenda is not a normal". After analyzing the information the detectives positively identified that Brenda was the guilty one. You need to justify why the detective conclusion was true.

Explanation / Answer

Let' start with Amy, since Amy says that she is innocent, this means that if she is a knight and telling the truth then she is innocent which is contradiction, So now Amy is eliminated she is innocent but not knight and definitely not the culprit.

Now we have Brenda and Claire left

So, suppose Claire is knight and she is the culprit this means that what she says is true but if her saying is true then this means that Brenda is not a normal, and since it is given only one knight is there in these three Brenda left with only one option to be in which is knave. But Brenda says that "What Amy says is true" which is true but we were told that knave always lie so this statement now can be concluded by saying that Claire is not a knight. Claire is normal and she is telling the truth. Now we left with only one option and that is Brenda and she is the one who committed the crime.

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