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UKMT Intermediate Mathematical Challenge, 2022

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

A function machine does the four operations shown in order: $\div 3$ , $-10$ , $\div 3$ , $-10$ . Iris inputs a positive integer and the output is also a positive integer. What is the smallest possible number which Iris could have input?

(A) $9$ (B) $84$ (C) $102$ (D) $120$ (E) $129$

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