Intellectual quiz.

What will happen in this thread? Here, I would like to see various tasks to test your ingenuity, logic, and a certain base of your knowledge. I recently came across some problems from math Olympiads. I need to submit them soon, but I decided to find a use for them, besides just reading them. Since I have the answers and descriptions of the correct solutions, I will be a kind of judge. I also have problems from the Kangaroo 2008 competition (an international math competition), but, of course, I don't have the correct solutions. Therefore, it will not be about solving problems on a competitive basis, but about joint discussion and arriving at the correct result. Two heads are better than one, even if it's not pretty. Naturally, I won't be able to provide an endless stream of tasks, so I ask everyone who finds interesting tasks to post them here. And please try to make the tasks focus on reasoning, rather than general knowledge. Everyone knows what Wikipedia is. Everyone is familiar with search engines like Yandex, Rambler, etc., where you can easily find answers to questions like "what is the area of Russia?", "why does the DNA molecule not move out of the cell nucleus, but is copied in parts in the form of mRNA?" and so on. Here is a description of my idea. First, vote on whether this quiz is needed at all. Next, if you voted for "Yes," then reply, indicating whether you would participate in such an event and whether you could share some tasks. After reading the posts and looking at the voting results, I will be able to draw a conclusion about the feasibility of this thread. If so, we will start the quiz; otherwise, I will ask the moderators to delete it.