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?

If all 200 people polled are knights there would be a total of 200 yes votes.  As the total yes votes is 258, 142 people answered yes once and 58 people answered yes twice.  So 58 liars.

As Alex gets 112 votes and the 58 liars could have said yes for Alex, at least 54 knights must have voted for him.

Similarly, at least 24 knights said yes for Bert and 6 knights said yes for Carl.

 

Posted by Nosher on 2005-09-30 02:41:13