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?

The primary flaw is that no Knight in the mixed group could say "We are all Knights" because this is not a true statement but rather each person in the mixed group could say "I am a Knight".

No such restriction is placed on Switchkins apparently. When making statements as a Switchkin the statements can be true or false, but the act of making the statement has the repercussion of transforming their nature.

Overall for clarity, the problem should be rephrased to have each member of each group say "I am a _____."

Posted by Eric on 2006-07-18 16:54:08