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?

To the last question, only an untruthful knave would claim to be a liar.  Thus there are eight knaves who were untruthful on the first and third questions while truthful on the second.

To the first question, only a truthful knave would answer 'no' to being a knight.  Thus there are eight knaves who were truthful on the first and third questions while untruthful on the second.

To the second question, there are eight truthful knaves who answered 'yes'.  The other four 'yes' responses could only come from liars.  The group is comprised as such:

Knights - 5

Knaves - 16

Liars - 4 

Posted by hoodat on 2007-06-11 00:48:47