Maths on the Back of an Envelope: Clever ways to (roughly) calculate anything

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1  Cover (#ube9b5bb8-b01d-57f4-8048-036dba1a0d71)

2  Frontmatter (#u893be14e-95f5-5740-afd9-b8d58d8996fc)

3  Begin Reading (#u893be14e-95f5-5740-afd9-b8d58d8996fc)

4  Table of Contents (#u4ad50bbf-de7a-518c-8447-bda80dc9bac9)

PROLOGUE

HOW MANY CATS?

A few years ago, at a school event, I asked the audience of teenagers to submit some estimation questions that I would then attempt to answer live on stage. One pupil posed this simple question: ‘How many cats are there in the world?’

Cats are always a popular topic, so I took it on.

My thinking went like this:

Let’s assume that most cats are domestic.

Some people have more than one cat, but usually a household has only one cat, if any at all.

In the UK, and thinking of my own street as an example, it seems reasonable to suppose that there might be one cat in every five households.

And, if a household contains on average two people, that means there is one cat for every 10 people.

So, with 70 million people in the UK, let’s say that there are, perhaps, seven million cats in the UK.

So far, so good. But what about the number of cats in the rest of the world? It seems unlikely that cats are as popular in countries like India or China as they are in the UK (although what would I know? Remember, this is purely guesswork on my part), therefore, I’d expect the ratio across the world to be smaller than it is in the UK – maybe one cat for every 20 people?

So, with eight billion people in the world, that suggests there are maybe:

8 billion ÷ 20 = 400 million cats.

It doesn’t seem an outrageous number.

That was the figure I suggested, anyway.

A member of the audience put his hand up.

‘The real number is 600 million,’ he said.

‘Really – how do you know?’