Problem

Source:

Tags: inequalities, induction, algebra unsolved, algebra



Given integer $n\geq 2$ and real numbers $x_1,x_2,\cdots, x_n$ in the interval $[0,1]$. Prove that there exist real numbers $a_0,a_1,\cdots,a_n$ satisfying the following conditions: (1) $a_0+a_n=0$; (2) $|a_i|\leq 1$, for $i=0,1,\cdots,n$; (3) $|a_i-a_{i-1}|=x_i$, for $i=1,2,\cdots,n$.