Infamy
There are a group of 6 people (A, B, C, D, E, and F) , and each person is able to recognize 2 people from this set. The following are a list of hints that describe the relationships between the six people.
Rules:
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No person knows someone who knows them back, EXCEPT Person A .
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No person is known by more than two people , except for Person B, who is known by three people. Everyone knows ONLY two people.
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By the logic of this puzzle, no one knows themselves.
Relations:
-Person D knows Person C and Person F.
-Person A does NOT know Person D, but Person D knows the person who knows Person F.
-Person E does NOT know Person B, but the opposite is false (i.e. Person B knows Person E).
-Person F knows Person A.
-Person F knows Person B, but Person B does not recognize Person C.
-Person A does NOT know Person C.
-Person E does NOT know Person D.
Who is the person that knows Person A back?
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1 solution
The real secret is not to figure out who knows who, but to know your options. The only options given are Person D, Person F, Person B, and Person E. Given the first relation, we know that, since no person knows more than three people (except Person B), that Person D is NOT an answer, and we can immediately cross it off as an option. The next hint lists that Person D knows someone who knows Person F, and using the logistic rule that people cannot know themselves, then Person C MUST know Person F, and since no one can know more than two people, we know that Person A does not know Person F, and therefore Person F is not an answer. The only two options left are Person B and Person E. Person A, through some process of deduction, knows BOTH of them, but the one thing that separates the two options are the relations with Person B. Person B does not know Person C, nor does Person B know himself. Person D knows F, and through deduction, Person C knows Person F as well, which means that Person B cannot know Person F. Person B cannot know more than two people, otherwise, someone else would break the rule of only being known by two other people. Therefore, Person B can only know Person D and Person E, leaving only Person E. Person E is the only person left, meaning that Person E knows Person A, and the other way around.