## Everything in its right place

By David Shaw, 9 October 2012

Image: Khalegh Mamakani and Frank Ruskey

**Do you own a dog? Do you ride a bike to school? Do you have black hair? Each of these questions divides people into two groups – you either have a dog, or you don’t. And if you had a large circle drawn on the ground, all the dog owners in your class could stand in that circle, so you could tell them apart from the people who don’t own a dog.**

What if you wanted to know who owned a dog, and who rode a bike to school? You’d need a second circle for bike riders. But you have to be careful where you draw the second circle. Bike-riding dog-owners also need a place to stand. You’ll need to make the circles overlap so they can be in both circles at the same time.

A diagram with overlapping areas like this is called a Venn diagram. Venn diagrams become much more complicated as you add more regions. Newroz, pictured above, is the first simple symmetric Venn diagram with 11 shapes. This means you could ask 11 yes or no questions, and everyone would have a place, no matter how they answered!

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