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?

Well, clearly the group that has all three types includes knights, so clearly they do not say "We are all Liars" or 'We are all Switchkins".  The group that has all three types must say "We are all knights".  Except no knight can say that because 2/3 of the group is not a Knight.  What they must say all say is "I am a Knight".  Apparently, a Switchkin is allowed to make this statement.  10 Liars in this Group.

So who can say "I am a liar"?  Not a knight, and not a liar.  Must be 30 switchkins,  if the problem makes any sense, but I'm not happy about it.  0 Liars in this group.

And the group that all says "I am a switchkin" must be 15 liars and 15 switchkins.

25 liars total.

Edited on July 17, 2006, 10:10 am

Posted by Steve Herman on 2006-07-17 10:09:23