I am a high school student interested in thinking about math. I don't know a lot of high-powered math (I only know up to calculus), instead I focus on discrete topics related to math Olympiads (combinatorics, number theory, geometry etc). Olympiad problems typically take 2-3 hours to solve. I want to start thinking about interesting problems over extended periods of time.
So I am wondering where I can find a bank of problems that satisfy the following criteria: they are simply stated, related to discrete topics (not graduate level math please), and are difficult enough that they cannot be solved in a day, but not as difficult as full fledged research problems. I am not talking about open problems nessecarily; I don't want to think about something like the Collatz conjecture, since that is too difficult as its been open for a long time.
I am sorry if I'm not being clear, but I dont know what more specifics I can give. Maybe someone can help me narrow down what I'm actually asking?