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Counting the Types (Posted on 2007-05-31) Difficulty: 2 of 5
A group of 25 consists of knights, knaves and liars. Each was asked two questions. 17 answered truthfully to the first question and 6 answered truthfully to the second.

What can be determined about the number of knights and liars in the group?

See The Solution Submitted by Brian Smith    
Rating: 2.5000 (2 votes)

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Solution solution-ish | Comment 1 of 4

Since there are only 23 true statements, at least 2 people lied twice.  Therefore there are at a minimum 2 liars.

Arranging the other 23 people:

  All could be knaves. 

  For every knight added to the group of 23, 1 liar must be added.

  Maximum number of knights: 6 (implies 11 knaves 8 liars)

  Maximum number of liars: 8 (same logic)

#liars = #knights + 2


  Posted by Leming on 2007-05-31 11:46:43
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