2021 WSMO Speed Round/Problem 1

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Problem

Let $f^1(x)=(x-1)^2$, and let $f^n(x)=f^1(f^{n-1}(x))$. Find the value of $|f^7(2)|$.

Solution (bash)

Note that |f7(2)|=f(f(f(f(f(f(f(2)))))))=f(f(f(f(f(f((21)2))))))=f(f(f(f(f(f(1))))))=f(f(f(f(f((11)2)))))=f(f(f(f(f(0)))))=f(f(f(f((01)2))))=f(f(f(f(1))))=f(f(f((11)2)))=f(f(f(0)))=f(f((01)2))=f(f(1))=f((11)2)=f(0)=(01)2=1