Explainer

What is a Venn diagram?

The simple picture behind the game, and where it came from.

A Venn diagram is a drawing that shows how groups of things relate to each other. Each group is drawn as a circle. Things that belong to a group go inside its circle, and things that belong to two groups at once go where the circles overlap.

Reading one

Look at the picture above. The left circle holds words that start with C. The right circle holds words that have a double letter. Because the circles overlap, the diagram has three regions inside it plus the space outside:

• Left only: starts with C but has no double letter, like cat and cold.
• Right only: has a double letter but does not start with C, like moon and ball.
• The middle: both at once, like coffee and cliff.
• Outside: neither, like dog.

In maths, the middle region is called the intersection of the two groups, often written with the symbol ∩. Everything inside either circle together is the union, written ∪.

Where they come from

The diagrams are named after John Venn, an English logician and philosopher who taught at the University of Cambridge. He described them in 1880 as a way to picture logical statements, building on older circle drawings used by mathematicians such as Leonhard Euler. Venn's version always draws every possible overlap, even ones that turn out to be empty, which makes them especially useful for reasoning.

Why they are everywhere

Venn diagrams are taught in primary school because they make sorting visible. Since then they have spread into statistics, biology, business planning and design, and they are a favourite format for jokes: two circles labelled with things people love, and something funny in the middle.

How Venn-acular uses them

Each daily puzzle is a two-circle Venn diagram with a rule about words on each circle. You fill the diagram yourself by typing words. Words in one circle score 5 points and words in the intersection score 15, so the game is really a race to find the overlap. To keep things easy to read, a starts with rule always sits on the left circle and an ends with rule always sits on the right.

Two rules that can never overlap are never paired. A word cannot start with both B and C, so those two rules never appear together. Every puzzle is checked so that plenty of everyday words land in the middle.