2021 JMC 10 Problems/Problem 3
Problem
A group of people are either honest or liars, where honest people always tell the truth and liars always lie. People
stand in a line, and person
calls
a liar where
Out of these eight people, how many liars are there?
Solution
If one calls
a liar, then only one of
can be a liar. If both are liars, we have a contradiction, because a liar would call another liar a truth teller. Likewise,
cannot both be truth tellers. We must have an alternating sequence of truth tellers and liars, so there are
liars.