Determine knights and knaves roles

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Determine knights and knaves roles states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Determine knights and knaves roles

Company: SIG (Susquehanna)

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Technical Screen

##### Question On an island of Knights (always tell the truth) and Knaves (always lie), you meet two people A and B. B says to A: "You always lie". Considering the four possible assignments of roles (A is Knave, B is Knight; A is Knight, B is Knave; A is Knave, B is Knave; A is Knight, B is Knight), determine which assignment(s) are logically consistent and explain your reasoning.

Overview: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Determine knights and knaves roles states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025
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Determine knights and knaves roles

Knights and Knaves Logic Puzzle

Context

On an island, each person is either:

  • Knight: always tells the truth.
  • Knave: always lies.

You meet two people, A and B. B says to A: “You always lie.”

Task

Evaluate the logical consistency of each possible assignment of roles to A and B:

(a) A is Knave; B is Knight (b) A is Knight; B is Knave (c) A is Knave; B is Knave (d) A is Knight; B is Knight

Determine which assignment(s) are logically consistent and explain why.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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