Pick a whole number. If it’s even, halve it; if it’s odd, triple it and add one. Keep going. Start at 6 and you’re home at 1 in eight steps. Start at 27 and the walk takes 111 steps, climbing as high as 9,232 before it finally comes down. Computers have run the rule on every starting number into the hundreds of billions of billions, and every one of them has ended at 1. Nobody has proved that they all do. It’s a strange place for a rule this short to leave us: we have watched every number we’ve ever tried find its way home, and we still can’t say why any of them knew the way.