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|x - 1| + |x - 2| +... + |x - 2001| = a exactly one solution

Source: 2001 Estonia National Olympiad Final Round grade 9 p4

March 12, 2020
algebraequationabsolute value

Problem Statement

It is known that the equation∣x−1∣+∣x−2∣+...+∣x−2001∣=a |x - 1| + |x - 2| +... + |x - 2001| = a has exactly one solution. Find aa.
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