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MathNet 2023-part-04 — 191 problems (EN–VI) Question 151

Math Olympiad Vault · MathNet 2023-part-04 — 191 problems (EN–VI)

Question 151

For each positive integer $n$, define the function $f_{n}(x) = |n - x|$. How many real solutions are there to
$$
\left(f_{1} \circ f_{2} \circ \cdots \circ f_{24} \circ f_{25}\right)(x) = 0?
$$