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?

  • $\begingroup$ Are there any odd perfect numbers? $\endgroup$
    – Eoin
    Nov 4, 2014 at 5:11
  • $\begingroup$ @Eoin Also, how many even perfect numbers exist? Also, how many twin primes are there? $\endgroup$
    – user109879
    Nov 4, 2014 at 5:14
  • 3
    $\begingroup$ You could go through some questions on this very site. $\endgroup$ Nov 4, 2014 at 5:48
  • 2
    $\begingroup$ @Callus: Why don't you post this question? $\endgroup$
    – user170039
    Nov 4, 2014 at 15:43
  • 1
    $\begingroup$ Why is there such a systematic attempt to discourage interest in mathematics? $\endgroup$ Nov 11, 2014 at 4:28

1 Answer 1


You could go to different university course pages and look for their undergraduate discrete math course. They are generally accessible to the public.

For exmaple:




And there are plenty more, have fun!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.