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?

How many knights were in the group?

x-number of knights

y-number of liers

there are 200 peoples in the group

x+y=200

 

the knight will say "yes" ones - the lier will say "yes" twice -the total of "yes" is 112+82+64=258

x+2y=258

from the last two facts

y=58

x=200-58=142

At least how many knights said they would vote for Alex? For Bert? For Carl?

in the worst case all of the liers will vote in faver of one of them so

for Alex_ 122-58=64

for bert_ 82-58=24

for carl_64-58=6

Posted by george on 2005-10-04 19:43:59