Algebra · Absolute value · Nested equations · Case analysis
Determine how many distinct solutions the equation
\[ \Bigl| \bigl| \cdots \bigl| \bigl| |x| - 1 \bigr| - 2 \bigr| - \cdots - 2016 \bigr| - 2017 \Bigr| = 2017 \]
has, where the constants \(1, 2, \dots, 2017\) are subtracted in turn and an absolute value is taken after each subtraction.
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Serbian Municipal Competition 2017, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source