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?

a liar  will  be supporting any one among three of them ...so a liar will vote only for the rest of the 2  mayors...that means each liar will vote twice.
so the extra votes given will be the no: of liars i.e.58
now let the total no of liars be x+y+z =58
x liars are on alex side..i.e they will vote for bert and carl
y liars are on bert side ..i.e they will vote to alex and carl
and z are on the carls side

now knights in voters that vote for alex= 112 -y-z
'''''''''''----------''''''''''''''''do'''''''''''''''''bert =82 -x -z
--------------------do-----------------carl = 64 -x-y
atleast knights that will vote for alex= 112 - 58 because y+z can have a max value of 58..therefore ans is 64
similarly for bert  82-58=24 and carl = 64-58=6
thanx
Dilip

Posted by dilip on 2005-10-04 09:12:03