On Halloween 31 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.
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Are you a truth-teller? The principal gave a piece of candy to each of the 22 children who answered yes.
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Are you an alternater? The principal gave a piece of candy to each of the 15 children who answered yes.
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Are you a liar? The principal gave a piece of candy to each of the 9 children who answered yes.
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How many pieces of candy in all did the principal give to the children who always tell the truth?
Answer Choices
A. 7
B. 12
C. 21
D. 27
E. 31