There are 123 tenants living in an apartment building.
logic/liars.survey New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
There are 123 tenants living in an apartment building. Some of the
tenants always tell the truth to people who do surveys, and the others
always lie. There are three restaurants [Editor: word added] below this apartment: a pizza
parlor, a hamburger joint and a barbecue place. Each tenant has a
favorite restaurant.
One day a person doing a market survey phoned all the tenants and
asked each 3 questions:
a) Is the pizza parlor your favorite? 45 tenants answered "yes"
b) Is the hamburger joint your favorite? 67 tenants answered "yes"
c) Is the barbecue place your favorite? 89 tenants answered "yes"
How many of the 123 tenants were liars?
(Posted by Chris Cole for pehlee@tm.net.my)
Show solution
78 of the tenants are liars. Each liar is going to answer "Yes" to exactly 2 of the 3 questions asked; each truth-teller is going to answer "Yes" to exactly 1 of the 3. If x is the number of liars, we have 2x + (123 - x) = 45 + 67 + 89, or x = 78. -- Eric Farmer <efarmer@math.uiuc.edu>