$29$ quadratic polynomials $f_1(x), \ldots, f_{29}(x)$ and $15$ real numbers $x_1<x_2<\ldots<x_{15}$ are given. Prove that for some two given polynomials $f_i(x)$ and $f_j(x)$ the following inequality holds: $$\sum_{k=1}^{14} (f_i(x_{k+1})-f_i(x_k))(f_j(x_{k+1})-f_j(x_k))>0$$A. Voidelevich