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 half answer by lindsay)

The answer as all other predecessors have come up with is 58 liars.  You cannot divide 58 by 2 and get 29 liars - that is wrong.  If all 200 were speaking the truth, you have a total of 200 votes.  If 199 were true and 1 was a liar, the liar gets 2 votes (i.e., for example, NO to A, YESto B and YES to C.  Therefore, 2 votes).  Total is 199+2 = 201.  Extrapolating, 198 knights = 198 votes, 2 liars = 4 votes.  Total = 198+4 = 202.  Therefore, for every liar, there is one extra vote over 200 (pattern logic or trial an error/induction).  Hence, if there are 258 votes, there are 58 liars.  If there were 200 liars, there would be 400 votes.

Someone also mispelt "LIAR" as "LIER".  Pl correct.

Posted by Mad on 2005-10-21 00:21:33