All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

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)

Comments: ( Back to comment list | You must be logged in to post comments.)
No Subject | Comment 6 of 13 |
Obviously, the group which says 'we are all liars' is all switchkins.  If there were any knights, they would be lying, and if there were any liars, they would be telling the truth.  That makes 30 liars so far.

Liars: 30

If then follows that there cannot be any knights in the group which says they are all switchkins, as they would be lying.  This group must then be the group composed of two types - liars and switchkins.  This adds 15 liars.

Liars: 45

Then, the last group, which says that they are all knights, must be composed of ten liars, ten switchkins, and ten knights.  This adds ten liars.

Liars: 55

  Posted by thegnome54 on 2006-07-27 23:35:09
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information