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

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!


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