Algebra · Absolute value · Piecewise linear functions · Minimization · Median
Real numbers \(a_1 < a_2 < \cdots < a_n\) are given. Find every real number \(x\) for which the expression
\[ |x - a_1| + |x - a_2| + \cdots + |x - a_n| \]
takes its smallest value.
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Serbian Municipal Competition 2001, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source