Take a look at the image below. It’s a collection of bugs and creepy-crawlies of different shapes and sizes. Take a moment to categorize them by similarity into a number of groups. This isn’t a trick question. Start with grouping the spiders together. Images via Google Image Search, labelled for reuse Done? While there’s not necessarily a “correct” answer here, it’s most likely you split the bugs into four clusters . The spiders in one cluster, the pair of snails in another, the butterflies and moth into one, and the trio of wasps and bees into one more. That wasn’t too bad, was it? You could probably do the same with twice as many bugs, right? If you had a bit of time to spare — or a passion for entomology — you could probably even do the same with a hundred bugs. For a machine though, grouping ten objects into however many meaningful clusters is no small task, thanks to a mind-bending branch of maths called combinatorics , which tells us th...