កំសាន្តសំនូរ​ តក្កវិទ្យា

Problem:

Of three men one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is who. You may ask three yes/no question to determine who is who. If you ask the same question to more than one person you must count it as question used for each person whom you ask.

What three questions should you ask?

Answer:

There are six possible sceanarios:

         Truth  Lying  Random
         Guy    Guy    Guy
         -----  -----  ------
I          A      B      C
II         A      C      B
III        B      A      C
IV         B      C      A
V          C      A      B
VI         C      B      A

Label the three men A, B, and C and tell each man who is what letter.

• Step 1: Ask A, “Is B more likely to tell the truth than C?” If yes go to step 2, if no go to step 5.
• Step 2: Ask C, “Are you the random guy?” If yes go to step 3, if no go to step 4.
• Step 3: Ask C, “Is A the truth guy?” If yes then scenario IV, if no then scenario II.
• Step 4: Ask C, “Is A the lying guy?” If yes then scenario V, if no then scenario VI.
• Step 5: Ask B, “Are you the random guy?” If yes then step 6, if no then step 7.
• Step 6: Ask B, “Is A the truth guy?” If yes then scenario VI, if no then scenario I.
• Step 7: Ask B, “Is A the lying guy?” If yes then scenario III, if no then scenario IV.