The 3 gods riddle
The Three Gods Riddle, also known as the “Hardest Logic Puzzle Ever,” is a challenging puzzle that requires logical reasoning and a strategic approach. Here’s a recap of the riddle and its solution:
The Riddle:
You are faced with three gods: True, False, and Random.
- True always tells the truth.
- False always lies.
- Random answers randomly, either truthfully or falsely.
Your task is to determine the identities of the gods (which one is True, which one is False, and which one is Random) by asking three yes-or-no questions. However, there are complications:
- Each question must be directed to exactly one god.
- The gods understand your language, but they respond in their own language, where “ja” and “da” mean “yes” and “no,” but you don’t know which word means which.
Solution:
The solution involves using logical constructs and framing the questions in a way that works regardless of which god you’re speaking to. Here’s how:
Step 1: Understand the Key Logical Tool
A key tool is the self-referential question:
“If I asked you [X], would you say ‘ja’?”
This question ensures that even if you don’t know whether “ja” means “yes” or “no,” the structure of the question handles both possibilities.
Step 2: Handle Random’s Behavior
To neutralize Random’s unpredictability, the structure of the questions ensures you get meaningful answers regardless of which god you ask.
The Questions:
Let the gods be A, B, and C. You can ask them the following questions:
To God A:
“If I asked you, ‘Is B Random?’, would you say ‘ja’?”
This question helps you distinguish between Random and a consistent responder (True or False).
To God B:
“If I asked you, ‘Are you True?’, would you say ‘ja’?”
This identifies whether B is True or False.
To God C:
“If I asked you, ‘Is A Random?’, would you say ‘ja’?”
This resolves the identity of C.
Key Points:
- The self-referential nature of the questions ensures consistency even when you don’t know the meanings of “ja” and “da.”
- By carefully analyzing the answers, you can deduce the identities of True, False, and Random.
Now let’s deduce the identities step by step based on the answers:
From Question 1:
- If you ask God A, “If I asked you, ‘Is B Random?’, would you say ‘ja’?”, and get an answer, you will be able to determine whether A is True, False, or Random. Here’s why:
- If the answer is consistent (either “ja” or “da”), it means A is either True or False.
- If the answer is random, it means A is Random.
From Question 2:
- If you ask God B, “If I asked you, ‘Are you True?’, would you say ‘ja’?”, this helps you narrow down whether B is True or False:
- If the answer is consistent (either “ja” or “da”), it tells you that B is either True or False.
- If the answer is random, it means B is Random.
From Question 3:
- If you ask God C, “If I asked you, ‘Is A Random?’, would you say ‘ja’?”, this will also help you determine whether C is True or False based on the answer’s consistency.
Conclusion:
- By comparing the answers you get from all three gods, you will be able to deduce the identities of True, False, and Random. Each question helps eliminate possibilities until you’re left with the correct identity for each god.
Example Walkthrough:
Let’s assume the gods’ answers to these questions are as follows:
- A’s answer to Question 1: “ja”
- B’s answer to Question 2: “da”
- C’s answer to Question 3: “ja”
Now, let’s break down these answers:
Question 1: “If I asked you, ‘Is B Random?’, would you say ‘ja’?” (asked to God A)
- If A is True: A would truthfully answer the question about B. If B is Random, A would answer “ja”. If B is not Random, A would answer “da”.
- If A is False: A would lie about whether B is Random. If B is Random, A would lie and say “da”. If B is not Random, A would lie and say “ja”.
- If A is Random: The answer could be either “ja” or “da” because Random answers randomly.
Interpretation: Since A says “ja”, there are two possibilities:
- A could be True, and B could be Random (because A would truthfully say “ja” if B is Random).
- A could be False, and B could not be Random (because A would lie about B being Random and say “ja” if B is not Random).
At this point, we need more information to determine if A is True or False.
Question 2: “If I asked you, ‘Are you True?’, would you say ‘ja’?” (asked to God B)
- If B is True: B would truthfully answer that they are True, so B would say “ja”.
- If B is False: B would lie about being True, so B would say “ja” (because they are not True, but would lie and say “ja”).
- If B is Random: The answer could be either “ja” or “da” because Random answers randomly.
Interpretation: B says “da”, which eliminates Random as a possibility for B (since Random could have answered either way). Now, there are two possibilities:
- B is False: False would lie and say “ja”, but since B said “da”, this tells us B is True.
- B could be True, and B truthfully says “ja” (this works too, but we have narrowed down B to True).
Question 3: “If I asked you, ‘Is A Random?’, would you say ‘ja’?” (asked to God C)
- If C is True: C would truthfully answer whether A is Random. If A is Random, C would say “ja”; if A is not Random, C would say “da”.
- If C is False: C would lie about whether A is Random. If A is Random, C would lie and say “da”; if A is not Random, C would lie and say “ja”.
- If C is Random: The answer could be either “ja” or “da” because Random answers randomly.
Interpretation: C says “ja”. This means:
- If C is True, then A must be Random.
- If C is False, then A must not be Random, but that conflicts with the rest of the logic (since we know that A was possibly identified as Random).
Given this, it’s clear that C is True, and A is Random.
Final Conclusion:
- A is Random (from C’s answer and A’s inconsistent answers).
- B is True (from B’s answer, which is consistent with the truth).
- C is False (since C’s answer, “ja,” fits the pattern of False lying).
Final Identities:
- A is Random.
- B is True.
- C is False.
More clever riddles with answers.