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Suppose:

  • I am a 'problem-solver' rather than a 'theory-builder'
  • I am an undergraduate student
  • I have a passion for solving mathematical problems
  • The homework I get is not satisfying (in the sense that the problems are computing-problems rather than problems that require creative thinking), and I get far too little homework

Where can I find interesting problems (that require creative thinking) if I want to have fun solving mathematical problems and to practice problem-solving? Are there lists/books of such problems?

Furthermore, suppose I want to know how it is to do research.

Are there lists of the kind "open problems which can be understood by undergraduates". I guess these open problems should be in the fields of "discrete mathematics/combinatorics" and "graph theory".

I only found: http://dimacs.rutgers.edu/~hochberg/undopen/

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closed as off-topic by Will Jagy, András Bátkai, R W, user9072, Marco Golla Dec 11 '15 at 19:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Will Jagy, R W, Marco Golla
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Not especially famous, long-open problems which anyone can understand mathoverflow.net/questions/100265/… $\endgroup$ – joro Dec 11 '15 at 17:31
  • $\begingroup$ I think, "long-open" questions are not the kind of problems I am searching for. Is it realistic for an undergraduate to solve "long-open" problems. In general, I would say no. Maybe there are some geniuses. $\endgroup$ – sdfaewrFAAEA Dec 11 '15 at 17:34
  • $\begingroup$ So are you asking for OPEN, but not open for long? $\endgroup$ – joro Dec 11 '15 at 17:37
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    $\begingroup$ This MSE posting might help: "Undergraduate Mathematics Research." To supplement the list you found, DIMACS Open problems for undergraduates, there is The Open Problems Project, the latter not specifically oriented to undergraduates. $\endgroup$ – Joseph O'Rourke Dec 11 '15 at 17:41
  • $\begingroup$ @Joseph: The second link is also in my post. Have you read my post/question? $\endgroup$ – sdfaewrFAAEA Dec 11 '15 at 17:44
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Richard Guy compiled a list of open problems in combinatorial game theory, available at http://library.msri.org/books/Book29/files/unsolved.pdf . His book "Unsolved problems in number theory" also contains parts which are more combinatorial in nature. In the realm of Davenport's constant there are many open problems, some of which are probably non-trivial but doable.

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There's a big list of open problems at:

Open Problem Garden

and a smaller list at:

Unsolved Problems and Rewards

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