Question

The country of Ost is inhabited only by people who either always tell the truth or always tell lies and who will respond to questions only with a "yes" or a "no." A tourist comes to a fork in a road, where one branch leads to the capital and the other does not. There is no sign indicating which fork to take, but Mr. Zed, who is a resident of Ost, comes along. What single question should the tourist ask Mr. Zed to determine which fork in the road to take?

Short answer

"If I asked if the left fork leads to the capital, would you say 'yes'?"

Step-by-step solution

Identify the Objective

The objective is to determine which fork in the road leads to the capital given that you can only ask Mr. Zed one question, and Mr. Zed either always tells the truth or always lies.

Identify a Reliable Question

The key to solving the problem is to find a question that Mr. Zed will answer 'yes' if the correct fork is taken, regardless of whether Mr. Zed tells the truth or lies.

Ask the Right Question

Ask Mr. Zed the following question: "If I asked you whether the left fork leads to the capital, would you say 'yes'?"

Analyze Possible Responses

- If Mr. Zed is a truth-teller and the left fork does lead to the capital, he would say 'yes'. - If Mr. Zed is a truth-teller and the left fork doesn't lead to the capital, he would say 'no'. - If Mr. Zed is a liar and the left fork does lead to the capital, he would lie about saying 'yes', resulting in a 'no'. - If Mr. Zed is a liar and the left fork doesn't lead to the capital, he would lie about saying 'no', resulting in a 'yes'.

Follow the Logic

From the analysis, you should take the left fork if Mr. Zed answers 'yes,' and take the right fork if he answers 'no.' Ask the same question for the right fork to confirm the direction if needed.

Key concepts

Truth-Tellers and Liars

In logic puzzles, like the one about directional forks and questions, characters typically either always tell the truth or always lie. These are known as truth-tellers and liars. Understanding these roles is crucial to solving puzzles effectively.

• Truth-Tellers: These individuals will always answer truthfully. When asked a question, their answer can be relied upon as a factual statement.
• Liars: These individuals always provide false answers to questions. If asked something, their response would be the opposite of the truth.

This binary system simplifies decision-making and helps engage in logical deducing since each person's response is predictably consistent. The key challenge is to construct your question so that it distinguishes truth-telling from lying clearly.

Decision Making

Decision making in these puzzles requires analyzing the scenario and strategically framing questions. Specifically, you're aiming to make an intelligent choice with limited information.

• Consider the goal: Here, the goal is to determine the right path to the capital.
• Identify constraints: In this case, the constraints include having only one question and interacting with someone who might be a liar or truth-teller.

In this logic problem, the decision-making process involves creatively asking a question that renders truthful guidance regardless of the respondent's nature. Such a question ensures the same answer is achieved through both truthfulness and deceit, simplifying the decision of which path to follow.

Yes-No Questions

The magic of yes-no questions in these puzzles lies in their simplicity and effectiveness. You are limited to asking questions that have straightforward 'yes' or 'no' answers, which demands precision in questioning.

Constructing Effective Yes-No Questions

To construct a suitable question, focus on ensuring that either response ("yes" or "no") is meaningful, irrespective of the respondent's truthfulness. In the given example, the tourist asks, "If I asked you whether the left fork leads to the capital, would you say 'yes'?"

• If the person is a truth-teller and the left fork is correct, they would say "yes".
• If the person is a liar and the left fork is correct, they would lie about saying "yes", thus responding "no".

This question efficiently extracts consistent and useful information, allowing the questioner to discern the correct path regardless of whether the respondent is a truth-teller or a liar. The elegance of yes-no questions in decision-making lies in their ability to cut through ambiguity with a single well-chosen query.