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Counting the Types 2 (Posted on 2007-06-05) Difficulty: 2 of 5
A group of 25 people consists of knights, knaves and liars. Each person was asked "Are you a knight?", and 17 responded yes. Each person was then asked "Are you a knave?", and 12 responded yes. And finally each person was asked "are you a liar?", and 8 responded yes.

How many knights, knaves and liars are in the group?

  Submitted by Brian Smith    
Rating: 4.0000 (1 votes)
Solution: (Hide)
Let K represent the number of knights, N1 the number of knaves with truth pattern TFT, N2 the number of knaves with truth pattern FTF, and L the number of liars.

From the third question: N2 = 8
From the second question: N2+L = 12, which makes L=4
From the first question: K+N2+L=17, which makes K=5
There are 25 people total: K+N1+N2+L = 25, which makes N1=8.

There are 5 knights, 16 knaves and 4 liars.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
nice problemAndre2010-05-27 17:45:41
nice onepleasance2008-12-15 10:08:18
SolutionSolutionhoodat2007-06-11 00:48:47
Some ThoughtsFurther ExplanationsK Sengupta2007-06-07 05:48:19
SolutionSolutionK Sengupta2007-06-05 11:41:22
SolutionSolutionRobby Goetschalckx2007-06-05 11:10:13
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