Alex, Bert, and Carl are running for mayor in a town populated by knights and liars. 200 people from the town were gathered as a polling group. Each person in the group favors exactly one candidate.

The first surveyor asked each person "Will you vote for Alex?". The second surveyor asked each person "Will you vote for Bert?". The third surveyor asked each person "Will you vote for Carl?".

The results were as follows: 112 said they would vote for Alex, 82 said they would vote for Bert, and 64 said they would vote for Carl.

How many knights were in the group? At least how many knights said they would vote for Alex? For Bert? For Carl?

(In reply to A quick guess by Nosher)

I got the same answer as Nosher, using similar logic:

58 liars
Alex gets at least 112-58 = 54 knight votes
Bert gets at least 82-58   = 24 knight votes
Carl gets at least 64-58   =   6 knight votes 

 

Posted by Ken Haley on 2005-09-30 05:14:19