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 Counting the Types 2 (Posted on 2007-06-05)
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.

 Subject Author Date nice problem Andre 2010-05-27 17:45:41 nice one pleasance 2008-12-15 10:08:18 Solution hoodat 2007-06-11 00:48:47 Further Explanations K Sengupta 2007-06-07 05:48:19 Solution K Sengupta 2007-06-05 11:41:22 Solution Robby Goetschalckx 2007-06-05 11:10:13

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