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2025 SSMO Tiebreaker Round Problems/Problem 3

Problem

Find the number of functions $f:\{1, 2, 3, 4, 5, 6, 7, 8\} \to \{1, 2, 3, 4\}$ such that $f(2f(x)) = f(x)$ for all $x \in \{1, 2, 3, 4, 5, 6, 7, 8\}$.

Solution

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