# The warming up game

The theater group began today with a warming up game.

Everyone has been assigned a role and is now either a bad guy who always lies, or a good guy who always tells the truth.

Max, who comes late, is asked to explore the roles of Jan and Jörg through yes-no questions.

"Are you both good guys ?", he asks Jan, who is full in his role, but his answer is not enough to know who has which role.

Max asks Jörg: "Is Jan a good guy ?" After Jörgs answer Max is fully informed and can name the roles of the two.

What counts ?

(A) Both are evil.
(B) Both are good.
(C) Jan is a good guy, Jörg a bad guy.
(D) Jörg is a good guy, Jan a bad guy.

## 3 Answers

Answer:

(D) Jörg is a good guy, Jan a bad guy.

Method:

If Jan answers "no," Max knows C. So Jan answered "yes" and C cannot be the case.
If Jörg answers "yes," Max does not know if A or B. So Jörg answered "no" and D must be the case.

• The big acting game I remember from high school was freeze tag, Jun 26, 2019 at 15:31

This answer is no different than @RShields, but it adds a visual to the answer that might be useful for some.

Let's explore every single possibility to find the answer.

If Jan says "yes" to the answer, then that means that there is no possible situation where C is possible. That means we have A, B, and D left. If Jörg then says yes, then if he was evil, A would be correct. However, if he was good, then B must have been the answer. This means we cannot be sure if both said yes. If Jörg said no, then if he was evil, A would be correct. But if he was good, then D must be correct. This means we cannot be sure if if Jan said yes and Jörg said no. This means we have disproved Jan saying yes to the first question.

So now...

If Jörg said yes, and he was evil then A must be correct. However if he was good, then B must be correct. This means Jörg did not say yes and Jan said no. We now know that Jörg said no and Jan said no. If Jörg was evil, this would mean C is true. If Jörg was good, then D is true. But if D was true, Jan would be evil and this would create a paradox because of the first question. This means that C is the answer.

Final Answer:

C is correct, and Jan and Jörg both said no.

• If Jan says "no," we actually don't satisfy the criterion, "Jan's answer is not enough to know both roles." Jun 26, 2019 at 23:35
• Yes, but becasuse Jan's answer does not satisfy the criterion we can go to Jorg's answer, which will satisfy the criterion!
– XDVV
Jun 27, 2019 at 6:54
• If Jan had answered "No". Then Max would be certain the roles of Jan and Jorg. The problem explicitly states that "his answer is not enough to know who has which role.". Therefore, Jan could not have answered "No" Jun 27, 2019 at 12:19
• Jan could certainly have said no, because we aren't sure whether Jan is good or bad.
– XDVV
Jun 27, 2019 at 16:07
• If Jan answers "no," Jan being good or bad becomes known, as @LeppyR64 said. Jun 27, 2019 at 16:53