Solution for #39

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:

Follow these steps to determine which possibility listed above is correct:

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.
2. Ask C, "Are you the random man?"
   • If yes, go to step 3.
   • If no, go to step 4.
3. Ask C, "Is A the truthteller?"
   • If yes, then scenario V is the case.
   • If no, then scenario II is the case.
4. Ask C, "Is A the liar?"
   • If yes, then scenario IV is the case.
   • If no, then scenario VI is the case.
5. Ask B, "Are you the random man?"
   • If yes, go to step 6.
   • If no, go to step 7.
6. Ask B, "Is A the truthteller?"
   • If yes, then scenario VI is the case.
   • If no, then scenario I is the case.
7. Ask B, "Is A the liar?"
   • If yes, then scenario III is the case.
   • 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.