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The warming up game

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6

$begingroup$

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.

logical-deduction liars

share|improve this question

edited 8 hours ago

jafe

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asked 9 hours ago

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New contributor

Matti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$

add a comment | 

6

$begingroup$

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.

logical-deduction liars

share|improve this question

edited 8 hours ago

jafe

30.9k44 gold badges8888 silver badges316316 bronze badges

asked 9 hours ago

MattiMatti

55011 silver badge1313 bronze badges

New contributor

Matti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

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.

logical-deduction liars

share|improve this question

edited 8 hours ago

jafe

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asked 9 hours ago

MattiMatti

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New contributor

Matti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

edited 8 hours ago

jafe

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asked 9 hours ago

MattiMatti

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share|improve this question

edited 8 hours ago

jafe

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asked 9 hours ago

MattiMatti

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edited 8 hours ago

jafe

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edited 8 hours ago

jafe

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asked 9 hours ago

MattiMatti

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asked 9 hours ago

MattiMatti

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2 Answers
2

active

oldest

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8

$begingroup$

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.

share|improve this answer

answered 9 hours ago

RShieldsRShields

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RShields is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  The big acting game I remember from high school was freeze tag,
  $endgroup$
  – RShields
  9 hours ago
  

  
  
  
  

add a comment | 

3

$begingroup$

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.

share|improve this answer

edited 8 hours ago

Adam

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answered 8 hours ago

XDVVXDVV

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New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If Jan says "no," we actually don't satisfy the criterion, "Jan's answer is not enough to know both roles."
  $endgroup$
  – RShields
  1 hour ago
  

  
  
  
  

add a comment | 

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8

$begingroup$

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.

share|improve this answer

answered 9 hours ago

RShieldsRShields

81611 silver badge99 bronze badges

New contributor

RShields is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  The big acting game I remember from high school was freeze tag,
  $endgroup$
  – RShields
  9 hours ago
  

  
  
  
  

add a comment | 

8

$begingroup$

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.

share|improve this answer

answered 9 hours ago

RShieldsRShields

81611 silver badge99 bronze badges

New contributor

RShields is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  The big acting game I remember from high school was freeze tag,
  $endgroup$
  – RShields
  9 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

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.

share|improve this answer

answered 9 hours ago

RShieldsRShields

81611 silver badge99 bronze badges

New contributor

RShields is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this answer

answered 9 hours ago

RShieldsRShields

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RShields is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered 9 hours ago

RShieldsRShields

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Check out our Code of Conduct.

answered 9 hours ago

RShieldsRShields

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3

$begingroup$

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.

share|improve this answer

edited 8 hours ago

Adam

50511 gold badge22 silver badges2121 bronze badges

answered 8 hours ago

XDVVXDVV

18877 bronze badges

New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If Jan says "no," we actually don't satisfy the criterion, "Jan's answer is not enough to know both roles."
  $endgroup$
  – RShields
  1 hour ago
  

  
  
  
  

add a comment | 

3

$begingroup$

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.

share|improve this answer

edited 8 hours ago

Adam

50511 gold badge22 silver badges2121 bronze badges

answered 8 hours ago

XDVVXDVV

18877 bronze badges

New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If Jan says "no," we actually don't satisfy the criterion, "Jan's answer is not enough to know both roles."
  $endgroup$
  – RShields
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

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.

share|improve this answer

edited 8 hours ago

Adam

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answered 8 hours ago

XDVVXDVV

18877 bronze badges

New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this answer

edited 8 hours ago

Adam

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answered 8 hours ago

XDVVXDVV

18877 bronze badges

New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 8 hours ago

Adam

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edited 8 hours ago

Adam

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answered 8 hours ago

XDVVXDVV

18877 bronze badges

New contributor

XDVV is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 8 hours ago

XDVVXDVV

18877 bronze badges