Popular Science

THE VARIANT

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In 1978, American philosophe­r and mathematic­ian Raymond Smullyan refined an existing logic puzzle to test deductive reasoning, or how well a person applies broad rules to arrive at a specific answer. In his “knights and knaves” scheme, problem solvers must determine the occupation­s of people on an island based on how they self-identify.

Instructio­ns: There is an island on which all the inhabitant­s are knights or knaves. Knights always tell the truth, and knaves always lie. Based on the statements, answer the question.

1. You encounter two people: Alison and Bernard.

Alison asserts, “At least one of us is a knave.”

What are Alison and Bernard?

2. Three people approach: Alvin, Byron, and Claudia.

Alvin says, “All three of us are knaves.”

Byron says, “Exactly one of us is a knight.”

What are Alvin, Byron, and Claudia?

3. A trio of island dwellers greet you on the beach: Alicia, Betty, and Clyde.

Two of the group are the same, either both knights or both knaves.

Alicia offers, “Betty is a knave.”

And Betty counters, “Alicia and Clyde are the same type.”

What is Clyde?

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