ZA-SAMO 2001 Problem 6

The unknown real numbers $x_1,x_2,\dots,x_n$ satisfy $x_1 < x_2 < \cdots < x_n,$ where $n \geq 3$ . The numbers $s$ , $t$ and $d_1,d_2,\dots,d_{n - 2}$ are given, such that $$\begin{aligned} s & = \sum\limits_{i = 1}^nx_i, t & = \sum\limits_{i = 1}^nx_i^2, d_i & = x_{i + 2} - x_i,\ \ i = 1,2,\dots,n - 2. \end{aligned}$$ For which $n$ is this information always sufficient to determine $x_1,x_2,\dots,x_n$ uniquely?