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Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes–no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja,[3] in some order. You do not know which word means which.​

Sagot :

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Answer:

This puzzle is a complex logic problem where you need to deduce the identities of three gods using three yes-or-no questions, despite not knowing how they respond with "yes" or "no" in their own language. Here’s how you can approach solving it:

### Step-by-Step Solution:

1. **Assign Labels to the Gods:**

- Let’s denote the gods as \( A \), \( B \), and \( C \).

- One of them is True (always tells the truth), one is False (always lies), and one is Random (answers randomly).

2. **Identify the Words "Da" and "Ja":**

- Let’s denote their words for "yes" and "no" as \( da \) and \( ja \), but we don’t know which is which.

3. **Formulating the Questions:**

- To navigate the unknown meaning of \( da \) and \( ja \), you need to frame your questions carefully so that the meaning of their answers can be determined indirectly.

### First Question:

Ask God A: "If I asked you 'Is B True?', would you say 'da'?"

- **Interpretation:**

- If \( A \) is True, then he will truthfully say whether he would say "da" to the question "Is B True?".

- If \( A \) is False, he would lie about whether he would say "da".

- If \( A \) is Random, his answer is unpredictable.

### Second Question:

Ask God B: "If I asked you 'Are you True?', would you say 'da'?"

- **Interpretation:**

- If \( B \) is True, he will truthfully answer.

- If \( B \) is False, he will lie about his answer.

- If \( B \) is Random, his answer is unpredictable.

### Third Question:

Ask God C: "If I asked you 'Is A False?', would you say 'da'?"

- **Interpretation:**

- If \( C \) is True, he will truthfully answer.

- If \( C \) is False, he will lie about his answer.

- If \( C \) is Random, his answer is unpredictable.

### Analysis:

1. **First Question Analysis:**

- Depending on the answer \( A \) gives, you can deduce if \( B \) is True or False.

- If the answer matches "da" (in whatever form), you might infer \( B \)’s role.

- Compare responses with other gods to cross-check.

2. **Second Question Analysis:**

- Helps identify \( B \)’s nature directly.

- Cross-check this with the first question’s response.

3. **Third Question Analysis:**

- Helps identify the nature of \( A \) indirectly via \( C \).

### Strategy to Determine Meanings of "Da" and "Ja":

- **Consistency Check:** True god’s answers will consistently align with the logical expectations of truth.

- **Cross-Verification:** Compare the answers of the questions between gods to see patterns that indicate who’s likely True, False, or Random.

### Key Insights:

- The Random god’s answers won’t fit any logical pattern, making the identification of True and False easier by elimination.

- Once True or False is identified, the role of the Random god becomes evident.

By combining logical deductions from these answers, you can identify the gods’ identities. It’s important to carefully track and analyze each response considering the inherent truthfulness or falsehood of each god.

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