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?
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.
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