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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?

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (1 votes)

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Some Thoughts Further Explanations | Comment 3 of 6 |
(In reply to Solution by K Sengupta)

Let us denote the knaves responding as 'ftf' as knave(I) and the
knaves responding as 'tft' as knave(II).

Then, as before, denoting the total number of knights, liars,
knave(I) and knave (II) respectively as N, R, A and B; we obtain the following table.

.
..................knight.....liar......knave(I)...knave(II).........Total #  
                                                                      "yes" responses

First Query.....Yes......Yes......Yes.............No...........R+N+A
Second Query..No......Yes......Yes............No...........R+A
Thirs Query.....No.......No.......Yes............No...........A

From the above table  in conjunction with the conditions of the problem, we observe that:

R+N+A+B = 25
R+N+A = 17
R+A = 12
A = 8

which leads to the same solution as in the previous post.

Edited on June 7, 2007, 5:55 am
  Posted by K Sengupta on 2007-06-07 05:48:19

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