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

Home > Logic > Liars and Knights
6 or less liars (Posted on 2015-11-13) Difficulty: 1 of 5
In a small village there are two kinds of people: liars and truthtellers.
Everybody knows everybody and everybody knows as well who is a liar and who’s a truth-teller.
I approach six villagers and pose the same question to each of them:
"How many liars are among you?"

I get six distinct answers (integers, of course) and deduce the true one.

How many liars are in that group?

Liars always lie and truthtellers never do.

See The Solution Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 16
First, ignoring that you were able to deduce the number:

There could be 6 liars, claiming 0, 1, 2, 3, 4 and 5 respectively.

There could be 5 liars, claiming 0, 1, 2, 3, 4 and 5 respectively, or any other set of answers that includes a 5.

So if the answers were 0, 1, 2, 3, 4, 5, you would not have been able to deduce whether there were 5 or 6 liars.

As there had to be at least 5 liars and there can't have been 6 liars, there must have been 5 liars, assuming there was in fact a set of answers that allowed you to make this conclusion.

Various of these possibilities exist, each including one person telling the truth, 5, and one person saying 6. Or, actually other weird possibilities exist, like 2, 4, 5, 7, 100, 111, but in that case you wouldn't have been able to tell if there were 5 or 6 liars, so there really were no "off the wall" answers above 6.

  Posted by Charlie on 2015-11-13 10:50:54
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (18)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information