JBMO-SL 2001 Problem 5

Let $x_k=\frac{k(k+1)}{2}$ for all integers $k\ge 1$ . Prove that for any integer $n \ge 10$ , between the numbers $A=x_1+x_2 + \ldots + x_{n-1}$ and $B=A+x_n$ there is at least one square.