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?

Sorry if this isn't in the correct format. I am rather new to this and not sure what's the 'proper form.'  However, from the puzzle, I think I've figured out how many knights there were (before I have to go running off to class).

The total number of votes cast was 258.  In order to negate the statement, 'I will vote for x,' you must say 'I will not vote for x, I will vote for y, and I will vote for z.'  Thus, each liar inflated the total number of votes by 2.  So, subtracting 200 from 258 gives a total of 58 inflated votes.  Dividing this by 2 gives the number of liars, 29.  Since 200 people were polled, then 200-29 = 171 knights in the group.

Posted by lindsay on 2005-10-10 13:07:24