It is known that $n$ is a positive integer, and the real number $x$ satisfies $$|1-|2-...|(n-1)-|n-x||...||=x.$$Find the value of $x$.
Source: China Northern MO 2011 p8 CNMO
Tags: algebra
It is known that $n$ is a positive integer, and the real number $x$ satisfies $$|1-|2-...|(n-1)-|n-x||...||=x.$$Find the value of $x$.