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Math Help - 16-region Venn diagram

  1. #1
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    16-region Venn diagram

    Find a way to place four circles (which may be of different sizes) to create a sixteen-region Venn diagram, or show that this cannot be done.
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  2. #2
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    Quote Originally Posted by scipa View Post
    Find a way to place four circles (which may be of different sizes) to create a sixteen-region Venn diagram, or show that this cannot be done.
    See attachment:

    RonL
    Attached Thumbnails Attached Thumbnails 16-region Venn diagram-gash.png  
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  3. #3
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    thanks... but is it possible with 4 circles? I'm quite certain it isn't since there are at most 8 regions in a 3-circle Venn diagram and creating 16 regions by adding a 4th circle requires the 4th circle to pass through every one of the 8 regions. How do I prove formally that it can't (or can) be done?
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