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Knights and Knaves: What does C say?

About the island of Knights and KnavesAbout Knights and Knaves and their consistencyKnights , Knaves and Spies - Part 1Knights , Knaves and Spies - Part 2Knights and knaves at a partyMeta Knights and Knaves Puzzle with HatsKnights, Knaves and Normals - the tough oneSolve the following knights and knaves problemKnights and Knaves Puzzle

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7

$begingroup$

You are on a fictional island with two types of people: knights who always tell the truth,
and knaves, who always lie. Three of the inhabitants - A, B, and C are standing in the
garden. A says, "B and C are of the same type" (B and C are both knaves or are both
knights.) Someone then asks C, "Are A and B of the same type?"
What does C answer?

logical-deduction liars

share|improve this question

edited 6 hours ago

Rand al'Thor

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asked 8 hours ago

53rleaves9953rleaves99

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$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Ahmed This is absolutely most definitely not a riddle. Please don't encourage misuse of tags.
  $endgroup$
  – Rand al'Thor
  6 hours ago
  

  
  
  
  

add a comment
 | 

7

$begingroup$

You are on a fictional island with two types of people: knights who always tell the truth,
and knaves, who always lie. Three of the inhabitants - A, B, and C are standing in the
garden. A says, "B and C are of the same type" (B and C are both knaves or are both
knights.) Someone then asks C, "Are A and B of the same type?"
What does C answer?

logical-deduction liars

share|improve this question

edited 6 hours ago

Rand al'Thor

76.2k1515 gold badges250250 silver badges501501 bronze badges

asked 8 hours ago

53rleaves9953rleaves99

3611 bronze badge

New contributor

53rleaves99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Ahmed This is absolutely most definitely not a riddle. Please don't encourage misuse of tags.
  $endgroup$
  – Rand al'Thor
  6 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

You are on a fictional island with two types of people: knights who always tell the truth,
and knaves, who always lie. Three of the inhabitants - A, B, and C are standing in the
garden. A says, "B and C are of the same type" (B and C are both knaves or are both
knights.) Someone then asks C, "Are A and B of the same type?"
What does C answer?

logical-deduction liars

share|improve this question

edited 6 hours ago

Rand al'Thor

76.2k1515 gold badges250250 silver badges501501 bronze badges

asked 8 hours ago

53rleaves9953rleaves99

3611 bronze badge

New contributor

53rleaves99 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 6 hours ago

Rand al'Thor

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asked 8 hours ago

53rleaves9953rleaves99

3611 bronze badge

New contributor

53rleaves99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 6 hours ago

Rand al'Thor

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asked 8 hours ago

53rleaves9953rleaves99

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edited 6 hours ago

Rand al'Thor

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edited 6 hours ago

Rand al'Thor

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asked 8 hours ago

53rleaves9953rleaves99

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Check out our Code of Conduct.

asked 8 hours ago

53rleaves9953rleaves99

3611 bronze badge

2 Answers
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11

$begingroup$

C will answer "Yes".

Assume A is a knight. Then B and C are either both knaves or both knights. If they are both knights, then all three are knights, and A and B are both therefore knights, and C will truthfully say that they are the same. If B and C are both knaves, then A and B are different, and C will lie and say they are the same.

Assume A is a knave. Then B and C are knight/knave or knave/knight. If C is a knave, then A and B are different, and C will lie and say they are the same. If C is a knight, then A and B are the same, and C will truthfully say they are. Thus, regardless of what the status of A and B are, C will answer that they are the same.

share|improve this answer

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is where this intuitively felt like it was going. But I didn't finish the full logical exhaustion of possibilities.
  $endgroup$
  – Cruncher
  5 hours ago
  

  
  
  
  

add a comment
 | 

0

$begingroup$

Suppose we refer to knights and true statements as "even" and knaves and false statements as "odd". Then the statement "Knights always tell the truth" and "Knaves always tell lies" can be recast as "A person and their statement always add up to even" (even + even is even, odd + odd is also even). Two people have the same type iff they add up to even. So A will say "B and C are the same type" only if the sum of "B and C are the same type" and A is even, i.e. A+(B+C) = even. This is completely symmetrical with respect to A, B, and C, so if A says "B and C are the same type", then C will say "A and B are the same type."

share|improve this answer

answered 4 hours ago

AcccumulationAcccumulation

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$endgroup$

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11

$begingroup$

C will answer "Yes".

Assume A is a knight. Then B and C are either both knaves or both knights. If they are both knights, then all three are knights, and A and B are both therefore knights, and C will truthfully say that they are the same. If B and C are both knaves, then A and B are different, and C will lie and say they are the same.

Assume A is a knave. Then B and C are knight/knave or knave/knight. If C is a knave, then A and B are different, and C will lie and say they are the same. If C is a knight, then A and B are the same, and C will truthfully say they are. Thus, regardless of what the status of A and B are, C will answer that they are the same.

share|improve this answer

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is where this intuitively felt like it was going. But I didn't finish the full logical exhaustion of possibilities.
  $endgroup$
  – Cruncher
  5 hours ago
  

  
  
  
  

add a comment
 | 

11

$begingroup$

C will answer "Yes".

Assume A is a knight. Then B and C are either both knaves or both knights. If they are both knights, then all three are knights, and A and B are both therefore knights, and C will truthfully say that they are the same. If B and C are both knaves, then A and B are different, and C will lie and say they are the same.

Assume A is a knave. Then B and C are knight/knave or knave/knight. If C is a knave, then A and B are different, and C will lie and say they are the same. If C is a knight, then A and B are the same, and C will truthfully say they are. Thus, regardless of what the status of A and B are, C will answer that they are the same.

share|improve this answer

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is where this intuitively felt like it was going. But I didn't finish the full logical exhaustion of possibilities.
  $endgroup$
  – Cruncher
  5 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

C will answer "Yes".

Assume A is a knight. Then B and C are either both knaves or both knights. If they are both knights, then all three are knights, and A and B are both therefore knights, and C will truthfully say that they are the same. If B and C are both knaves, then A and B are different, and C will lie and say they are the same.

Assume A is a knave. Then B and C are knight/knave or knave/knight. If C is a knave, then A and B are different, and C will lie and say they are the same. If C is a knight, then A and B are the same, and C will truthfully say they are. Thus, regardless of what the status of A and B are, C will answer that they are the same.

share|improve this answer

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

$endgroup$

share|improve this answer

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

answered 8 hours ago

Jeff ZeitlinJeff Zeitlin

3,32088 silver badges2525 bronze badges

0

$begingroup$

Suppose we refer to knights and true statements as "even" and knaves and false statements as "odd". Then the statement "Knights always tell the truth" and "Knaves always tell lies" can be recast as "A person and their statement always add up to even" (even + even is even, odd + odd is also even). Two people have the same type iff they add up to even. So A will say "B and C are the same type" only if the sum of "B and C are the same type" and A is even, i.e. A+(B+C) = even. This is completely symmetrical with respect to A, B, and C, so if A says "B and C are the same type", then C will say "A and B are the same type."

share|improve this answer

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges

$endgroup$

add a comment
 | 

0

$begingroup$

Suppose we refer to knights and true statements as "even" and knaves and false statements as "odd". Then the statement "Knights always tell the truth" and "Knaves always tell lies" can be recast as "A person and their statement always add up to even" (even + even is even, odd + odd is also even). Two people have the same type iff they add up to even. So A will say "B and C are the same type" only if the sum of "B and C are the same type" and A is even, i.e. A+(B+C) = even. This is completely symmetrical with respect to A, B, and C, so if A says "B and C are the same type", then C will say "A and B are the same type."

share|improve this answer

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

Suppose we refer to knights and true statements as "even" and knaves and false statements as "odd". Then the statement "Knights always tell the truth" and "Knaves always tell lies" can be recast as "A person and their statement always add up to even" (even + even is even, odd + odd is also even). Two people have the same type iff they add up to even. So A will say "B and C are the same type" only if the sum of "B and C are the same type" and A is even, i.e. A+(B+C) = even. This is completely symmetrical with respect to A, B, and C, so if A says "B and C are the same type", then C will say "A and B are the same type."

share|improve this answer

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges

$endgroup$

share|improve this answer

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges

answered 4 hours ago

AcccumulationAcccumulation

58422 silver badges1111 bronze badges