How many words to cover the world?

The radius of the earth is 6,371 km, and formula for the surface area of a sphere is 4πr², where r is the radius. Converting kilometres to metres, substituting for r and ignoring the fact that the earth isn't quite spherical, we get 4 x π x 6371000 x 6371000 which is almost exactly 5.1e14 (510,000,000,000,000) square metres. Dividing this by the size of a What3Words square (9 square metres) we get 5.67e13 (56,700,000,000,000) squares. If we have n words, we can make n³ different three-word sequences from them, and we need the value n³ to be at least 5.67e13 so every square on the earth can have its own address. Taking the cube root of 5.67e13, it turns out we need n to be at least 38,417.

The consensus on the web is that the average speaker of English understands around 30,000 to 40,000 words. Within those, there will be some that aren't suitable for What3Words (a lot of those have four letters) and some pairs that aren't suitable (including both "there" and "their" would invite confusion when the word sequences are spoken). But 38,417 is less than 40,000, so we can afford to lose a few.

What3Words addresses can often be amusing, even though they're composed of words that are innocent enough on their own. By all means go to what3words.com and have a look the addresses they've assigned to the three-metre squares in your home, but don't post the results online, because doing so is exactly equivalent to telling the whole world where you live, and then the burglars will only have to watch your Facebook feed for holiday snaps and they'll know when to call round.