Are we Knights or Knaves?

Logic Level 1

The Knight always tells the truth, the Knave always lies, and the Joker can either lie or tell the truth.

Susan and Thomas make the following statements:

Susan: I am a Knight.
Thomas: I am a Knave.
Susan: Thomas is a Knight.
Thomas: Susan is a Knave.

Which of the following statements must be true?

Thomas is a Joker Susan is a Knave Thomas is a Knave Thomas is a Knight Susan is a Knight Susan is a Joker

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Chung Kevin by Chung Kevin , 45, Australia

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4 solutions

Chung Kevin
Dec 28, 2016

All 3 types can say "I am a Knight", so we don't get additional information about Susan as yet.
Only the Joker can say "I am a Knave".
The third sentence tells us that Susan is lying, so she is not a knight.
The fourth sentence seems to provide no additional information.

Let's now consider the possible cases.

Susan Thomas
Joker Joker Logically consistent
Knave Joker Logically consistent

Thus, we can only conclude that Thomas is a Joker, but we do not know what Susan is.

13 Helpful 1 Interesting 2 Brilliant 0 Confused

Thomas is telling the truth about Susan being a Knave in the fourth statement.

Diana Bradish - 1 year, 2 months ago

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Yes, but Susan may also be another Joker, and Thomas might have told a lie about Joker Susan being a knave. Thus, the "no additional information".

Saya Suka - 3 months, 1 week ago

The only one who can say "I am a knave" is a Joker

5 Helpful 1 Interesting 1 Brilliant 0 Confused

For completeness, we should also ensure that the remaining options are not valid deductions.

Calvin Lin Staff - 4 years, 3 months ago
Shoaib Shafi
Mar 2, 2017

Both are joker... Both changed their statements so they must be joker...

1 Helpful 1 Interesting 1 Brilliant 0 Confused

Incorrect. Each person is saying 2 statements, and if they're not contradicting then the statements are not changed.

Digital Gaming 227 - 2 years, 3 months ago

Susan’s a Knave, because Thomas was telling the truth about her being a Knave.

Diana Bradish - 1 year, 2 months ago

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Susan's a knave OR a Joker, so Thomas's second statement is the truth about a knave Susan OR a lie about a Joker Susan.

Saya Suka - 3 months, 1 week ago
Saya Suka
Apr 25, 2021

Thomas : I am a Knave.
✓ Thomas made a Joker-specific false statement
✓ Thomas is a Joker

Susan : Thomas is a Knight.
✓ 🃏 Thomas is NOT a Knight
✓ Susan is lying with a generic lie
✓ Susan could have lied as a knave (by nature) or as another 🃏 (by choice)

Conclusions : Joker 🃏 Thomas is a true fact. Susan is NOT a Knight.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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