# Venn Diagrams

I like Venn diagrams. Growing up in the UK, my early schooling taught ‘Modern Mathematics’ so we created them from an early age.

John Venn, the mathematician they are named after, was a fellow Yorkshireman. Along with George Boole, and Augustus De Morgan, he developed theories of symbolic logic, set theory, probability, and statistics. These principles are key to most elements of computer science, and if you have ever had to write anything more than a trivial SQL statement, you will have leveraged these principles.

Here is a Venn diagram showing the overlap between Chemical Element Symbols and US state Abbreviations (because, why not?)

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## Puzzle

The other day I saw an interesting puzzle on math stack exchange.

In a village, 90% of people drink Tea, 80% drink Coffee, 70% drink Whiskey, and 60% drink Gin. Nobody drinks all four. What percentage of people drinks alcohol?

It’s one of those problems that you first think is easy to solve, then you think ‘hang on, there is not sufficient information’, but you plough on, and find there is an elegant answer.

If you add up the percentages (90%+80%+70%+60%) you get 300%. This means that the

*average*number of beverages per person is three. We are told that nobody imbibes all four beverages, so this means that nobody can drink*less than*three beverages (we know the average is three, so if nobody has more than three, nobody can have less than three); everyone has to drink__exactly__three types of drink.If everyone drinks exactly three drinks, then there is exactly one drink that everyone does not drink. This means there is nobody who doesn’t drink both whiskey and gin.

Therefore everyone in the village drinks alcohol.

Everyone in the village drinks alcohol!