Question 20
Prove that among every 42 numbers from the interval $[1, 10^6]$ it is possible to choose four numbers in such a way that for any permutation $(a, b, c, d)$ of these numbers, the following inequality holds:
$$
25(ab + cd)(ad + bc) \geq 16(ac + bd)^2.
$$
$$
25(ab + cd)(ad + bc) \geq 16(ac + bd)^2.
$$