2022 AMC 10A Problems/Problem 12
Problem 12
On Halloween 
children walked into the principal's office asking for candy. They
can be classified into three types: Some always lie; some always tell the truth; and
some alternately lie and tell the truth. The alternaters arbitrarily choose their first
response, either a lie or the truth, but each subsequent statement has the opposite
truth value from its predecessor. The principal asked everyone the same three
questions in this order.
"Are you a truth-teller?" The principal gave a piece of candy to each of the 
children who answered yes.
"Are you an alternater?" The principal gave a piece of candy to each of the 
children who answered yes.
"Are you a liar?" The principal gave a piece of candy to each of the 
children who
answered yes.
How many pieces of candy in all did the principal give to the children who always tell the truth?
