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

Home > Logic > Liars and Knights
Turn Tease (Posted on 2012-08-27) Difficulty: 1 of 5
In a remote island, all the inhabitants are either knights, who always speak truthfully or liars, who always speak falsely.

Ten natives of the island are engaged in a conversation. A visitor from a nearby island approaches the natives and, asks them: "How many of you are knights?"

Each of the ten natives answer in turn: 3, 2, 5, 7, 3, 0, 4, 4, 3, 5

In reality, how many of the ten natives are knights?

No Solution Yet Submitted by K Sengupta    
Rating: 1.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 5 |

They can't be all truth telling knights because they all give different answers.

So there is at least one liar.  Given this, and the fact that there are 6 different answers given, there are at least 5 liars, or at most 5 truth telling knights.

There can't be all liars, as there is the one person who did in fact say 0, and that would make him telling the truth.  This gives us the fact that there is at least one truth telling knight.  Given this, we know that at least one of the answers given is right, meaning that there are either 2, 3, or 5 truth telling knights. (0 and 7 have already been eliminated.)

Because the only answer given the same number of times is 3, then there are 3 truth telling knights.


  Posted by Joshua on 2012-08-27 15:10:04
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 (4)
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