The maths meme that has been distracting mathematicians for a century

A seemingly simple set of rules kicks off a kind of mathematical magic trick, which has kept great minds busy since the 1930s. Almost a century ago, a mathematician came up with a puzzle that was so seemingly simple and yet so fiendishly difficult that it has been distracting other mathematicians ever since. It has become a meme that jumps from brain to brain, with many people claiming to have solved it, only to have their hopes dashed as the proof unravels. And be warned - once I explain the rules, you will immediately want to start playing around with it yourself, and I take no responsibility for how much of your time you waste. It starts a bit like a magic trick.