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3Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.– MangaraCommented Aug 27, 2014 at 0:27
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2@Mangara, I have some reservations about "accessible problems that are still unresolved". That this is usefully so is a pleasant optimism, but I doubt that it is matched "in the fact".– paul garrettCommented Aug 27, 2014 at 1:25
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3I can only really speak for "the fact" my own field (computational geometry), but if we define an accessible problem as one whose problem statement can be easily understood by amateur mathematicians, many of the problems we study are indeed accessible.– MangaraCommented Aug 27, 2014 at 2:21
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1What @Mangara said. It is constantly surprising to me just how many accessible questions are open. The fact that a question is easy to understand is no indication that it is easy to solve!– JeffECommented Aug 27, 2014 at 11:54
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3@Mangara: Still, even if the problems look similar to contest problems, the experience of solving them is very different.– Nate EldredgeCommented Aug 27, 2014 at 17:41
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