On Christmas Eve, children walked into Santa's workshop asking for a gift. 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. Santa asked everyone the same three questions in this order:
"Are you a truth-teller?" Santa gave a gift to each of the children who answered yes.
"Are you an alternater?" Santa gave a gift to each of the children who answered yes.
"Are you a liar?" Santa gave a gift to each of the children who answered yes.
How many gifts in total did Santa give to the children?
55
62
69
76
83
