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?
(In reply to
answer by K Sengupta)
We will accept the caveat given in the comments - that:
"everybody in one group says, "I am a knight", everybody in another groanother group says, "I am a knight" and everybody in the remaining group says, " "I am a Switchkin."
Neither a knight or a liar will say that he is a liar.Therefore, only a Switchkin can claim to be a liar.So, each of the group claiming to be a liar must have the full strength of 30. Also, the said claim will transform these 30 switchkins to liars.
Again, a knight will never claim to be a Switchkin but nothing bars a liar or a Switchkin to make that claim.So, this group will have 15 each of switchkins and liars, with all the switchkins getting transformed to liars.
All three types can claim to be a knight. So the members of the group making the claim, "I am a knight" will consist of 10 of each type with the 10 switchkins being transformed to liars after the statement.
Consequently, the total number of liars in the group after this announcement is 30+15+10= 55.
Edited on July 5, 2022, 11:33 pm
Explanation to Puzzle Answer
