We're all mad here!

Logic Level 2

Everyone in Wonderland is either sane or mad. A sane person believes a statement if and only if it is true. A mad person believes a statement if and only if it is false.

Alice asked the King of Hearts whether or not the Queen of Hearts was mad. The King laughed and said, "I believe she believes she is mad!"

What can we conclude?

Exactly one of the King and Queen are mad The Queen is sane and the King is mad The King is mad The Queen is mad

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Maggie Miller by Maggie Miller , 27, USA

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4 solutions

Maggie Miller
Jul 17, 2015

If the Queen of Hearts is sane, then she will not believe she is mad. If the Queen of hearts is mad, then since she does not believe true statements, she will not believe she is mad. Therefore, the Queen of Hearts does not believe she is mad , so the King of Hearts believes a false statement. Then the King must be mad.

However, we cannot determine whether the Queen is sane or mad, as either way the King would believe that she believed she was mad.

19 Helpful 0 Interesting 0 Brilliant 2 Confused

the options should be more accurate i guess.... i opted that exactly one of the queen and king is MAD.. i was right ... " I THINK!!"... plz explain further..

Shreyansh Singh Solanki - 5 years, 9 months ago

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We can't conclude that exactly one is mad, since they might both be mad. That option is incorrect.

Maggie Miller - 5 years, 9 months ago

This part of the king's statement "she believes she is mad!" contradicts itself (whether queen is mad or sane) based on the givens, ;so that leads to King's statement being false which means he is "mad"

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Fahad Khan
Sep 20, 2015

king believes that queen is mad but not the queen itself

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Benjamin Becker
Aug 7, 2017
reality(queen) reality(king) believe(queen) believe(king)
mad mad sane mad
sane mad sane mad
mad sane sane sane
sane sane sane sane
0 Helpful 0 Interesting 0 Brilliant 0 Confused

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