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For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.
78
votes
Not especially famous, long-open problems which anyone can understand
I always enjoyed telling people about the Inscribed square problem :
Does every (Jordan) curve in the plane contain all four vertices of
some square?
Update: Here is a variation due to Helge Tverbe …