Don't Look at my Hat

What this logic-puzzle interview question tests

This is a medium-difficulty puzzle that appears in quant interviews to assess deductive reasoning and the ability to extract information from what people choose not to say. It rewards candidates who can work backwards from incomplete information and update beliefs based on the announcements of others.

The problem hinges on understanding what each person's statement reveals about the state of the hats they observe. When someone says they don't know their own hat color, that negative statement becomes positive information for the next person. Solving it requires careful case analysis: tracking which hat combinations are possible given the initial constraint, then eliminating scenarios as each person speaks.

• Backward induction and information cascades
• Reasoning about common knowledge
• Constraint elimination under incomplete observation