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AIME 1983 Problem 2

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Let f(x)=∣x−p∣+∣x−15∣+∣x−p−15∣f(x)=|x-p|+|x-15|+|x-p-15|, where 0<p<150 < p < 15. Determine the minimum value taken by f(x)f(x) for xx in the interval p≤x≤15p \leq x\leq15.

Dataset text AIME 1983 to 2026. Quoted with source.

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