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.
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?