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| ==Problem 12==
| | #redirect [[2022 AMC 12A Problems/Problem 9]] |
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| On Halloween <math>31</math> children walked into the principal's office asking for candy. They
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| can be classified into three types: Some always lie; some always tell the truth; and
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| some alternately lie and tell the truth. The alternaters arbitrarily choose their first
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| response, either a lie or the truth, but each subsequent statement has the opposite
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| truth value from its predecessor. The principal asked everyone the same three
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| questions in this order.
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| "Are you a truth-teller?" The principal gave a piece of candy to each of the <math>22</math>
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| children who answered yes.
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| "Are you an alternater?" The principal gave a piece of candy to each of the <math>15</math>
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| children who answered yes.
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| "Are you a liar?" The principal gave a piece of candy to each of the <math>9</math> children who
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| answered yes.
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| How many pieces of candy in all did the principal give to the children who always
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| tell the truth?
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| <math>\textbf{(A) } 7 \qquad \textbf{(B) } 12 \qquad \textbf{(C) } 21 \qquad \textbf{(D) } 27 \qquad \textbf{(E) } 31</math>
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| [[2022 AMC 10A Problems/Problem 12|Solution]] | |
