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?

There are 55 liars after the announcement.

The first group of 30 that are all the same type are Swtichkins - they say 'We are all Liars.'  Liars wouldn't say they are liars, nor would Knights.  They all become Liars at this point.

The second group of 30, which is an even number of two types are Liars and Switchkins.  They say 'We are all Switchkins'.  No new Liars born, but we still have the original 15 that were there to start.

The third group of 30, an even number of all three types makes the statement 'We are all Knights.'  So the 10 Switchkins becomes Knights, the Knights remain as such at a count of 10 and the Liars do the same.  So 10 Liars in the third group.

30 in the first group, 15 in the second, 10 in the third - that makes 55.

 

Posted by Sara on 2006-08-09 15:17:25