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Home > Logic > Liars and Knights
Land of Zoz (Posted on 2006-07-17) Difficulty: 3 of 5
In the land of Zoz, there are three types of people. In addition to the usual Knights and Liars, there are Switchkins who become whatever they say they are.

One morning, three groups of 30 gather. The first group has one type, the second group has an equal number of two types, and the third group has an equal number of all three types.

Everybody in one group says "We are all Knights", everybody in another group says "We are all Liars", and everybody in the remaining group says "We are all Switchkins."

How many Liars are there after this announcement?

No Solution Yet Submitted by Salil    
Rating: 3.3333 (3 votes)

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Agree with Steve and KARTHIK | Comment 8 of 13 |

I came to the same conclusion - 25 Liars.  My logic was a little shorter than KARTHIK's. 

What statement can Group 3 make?   Since knights are part of the group, they cannot say anything BUT "I am a knight".  That statement works for the liars and switchkins too.

So what statement can Groups 1 and 2 say, since Knights is taken?  There can be no knights in either group now either.  The group that says "I am a liar" cannot have liars in it, as they would be telling the truth, so it is all switchkins.  That leaves the last group, who says "I am a switchkin" to be half liars and half switchkins, since that works for the liars.

So we have 10 liars in the group of all three, and 15 liars in the group of two, for a total of 25.

  Posted by Bobbie Mieczkowski on 2006-07-28 16:29:58
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