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**Thought for the day**: To get the full meaning of some prompts, you need to take your time and pay attention to the details.

**Concepts**: Venn diagrams; sets and subsets; counting combinations; powers of 2 (possibly symmetry)

**Examples of noticing and wondering**

*I notice *four main rectangles: red, blue, yellow, and grey.*I notice *that the diagram has symmetry.*I notice *that this is a Venn diagram made of rectangles rather than circles.*I notice *that each region contains a unique combination of colors.*I notice *that there are sixteen regions (including the outside part that has no colors).*I wonder *if the Venn diagram is complete (contains every possible combination of the four colors).*I wonder *if there are other ways to create a complete 4-set Venn diagram.*I wonder *if I could make a 4-set Venn Diagram using only circles.*I wonder *how many regions a 5-set Venn diagram would need to have.*I wonder *if it is possible to make a 5-set Venn diagram.

** Notes**

Many people are familiar with two- and three-set Venn diagrams. Four-set diagrams may be less familiar, and it is surprisingly hard to create one that includes all possible combinations. Try making one using circles! Most people discover that at least two of the combinations are left out.

This prompt offers a great chance for students to study combinations. The number of regions in a complete Venn diagram follows an interesting pattern. Can you find it and discover what causes it?

**Number of Sets Number of Regions**

1 2

2 4

3 8

4 16

There are many other interesting things you might wonder! The following list just scratches the surface.

*I wonder *what is the best way to keep track of the regions so that I don't miss any.*I wonder *if a 5-set Venn diagram can have symmetry.*I wonder *if it is possible to make all *n-set* Venn diagrams (where *n *can be any counting number).