The discussion on Venn diagrams brought up a problem I had once encountered, but was too busy to think about much at the time.
The Venn diagrams I have used and/or seen up to now have been limited to at most three circles. With one, two, or three circles it is simple and natural to draw the circles in such a way that all possible subsets are represented. What does it look like if there are four circles? (Hint: How many distinct regoins should there be?) Can you draw it in such a way that no regions are "repeated"? Can it be done with circles, or do you have to bend one?
(I only know the answers to some of these questions so far.)
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