Is the method of cultural competition that relies on sharing the profits of (permissible) advertisements with the winners after drawing lots from the correct answers considered gambling or legitimate, and what is the legitimate alternative if it is gambling?

If the competition is free of charge and devoid of শরীয়াহ-prohibited elements, then there is no harm in it, and it is not considered the forbidden gambling (qimar). If the prize is provided by an external party and not by the contestants themselves, then there is no objection to it, as mentioned by Ibn 'Uthaymeen. However, if participation requires payment of money, then that falls under the forbidden gambling (maysir).