Truth n lie
Written on 12:57 am by Vja Students
Of three men, one always tells the truth, one always tells lies, and one answers "yes" or "no" randomly. Each man knows which one each of the others are. You may ask three yes/no questions, each of which may only be answered by one of the three men, after which you must be able to identify which man is which. How can you do it?
Ans: There are six possible scenarios. Let's call the first man A, the second man B, and the third man C. The six scenarios, then, are:
Scenario A B C
I Truthteller Liar Random Man
II Truthteller Random Man Liar
III Liar Truthteller Random Man
IV Liar Random Man Truthteller
V Random Man Truthteller Liar
VI Random Man Liar Truthteller
Follow these steps to determine which possibility listed above is correct:
1. Ask A, "Is B more likely to tell the truth than C?"
o If yes, go to step 2.
o If no, go to step 5.
2. Ask C, "Are you the random man?"
o If yes, go to step 3.
o If no, go to step 4.
3. Ask C, "Is A the truthteller?"
o If yes, then scenario V is the case.
o If no, then scenario II is the case.
4. Ask C, "Is A the liar?"
o If yes, then scenario IV is the case.
o If no, then scenario VI is the case.
5. Ask B, "Are you the random man?"
o If yes, go to step 6.
o If no, go to step 7.
6. Ask B, "Is A the truthteller?"
o If yes, then scenario VI is the case.
o If no, then scenario I is the case.
7. Ask B, "Is A the liar?"
o If yes, then scenario III is the case.
o If no, then scenario V is the case.
By following the steps above, you will only ever ask three questions in all, and the answers will determine the identities of the three men
