Brain Teasers and Logic Puzzles

# How do you solve a four circle venn diagram?

###### Wiki User

###### 2008-08-27 21:48:07

You can't create a Venn diagram with four circles.

Two circles intersect in at most two points, and each

intersection creates one new region. (Going clockwise around the

circle, the curve from each intersection to the next divides an

existing region into two.)

Since the fourth circle intersects the first three in at most 6

places, it creates at most 6 new regions; that's 14 total, but you

need 2^4 = 16 regions to represent all possible relationships

between four sets.

But you can create a Venn diagram for four sets with four

ellipses, because two ellipses can intersect in more than two

points.