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HMMT November 2024 E8

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Let

f(x)=∣∣⋯∣∣∣∣x∣−1∣−2∣−3∣−⋯∣−10∣f(x)=||\cdots||| | x|-1|-2|-3|-\cdots|-10|

Compute f(1)+f(2)+⋯+f(54)+f(55)f(1)+f(2)+\cdots+f(54)+f(55).

Dataset text NuminaMath olympiads. Quoted with source.

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