67. The Con Badge Problem
(With thanks to TT and IL for prompting me to think about this. Happy Pi Day.) Picture this: you're at a convention. You've got multiple badges to juggle - an attendee badge, two or three beautiful art badges to display, and maybe even an access or volunteer badge - so you've put them all on the same lanyard. In the morning, you carefully arrange them all facing the right way, put the lanyard on, and go out to the con. By noon, at least one badge will already have flipped backwards. By evening, another two have flipped backwards, and you could swear that you briefly saw one of them upside down. Over the course of the con, you fight a losing battle: you notice a backwards badge and flip it and it flips back on its own; you take off your lanyard altogether and carefully reorient all the badges correctly, and within an hour, half the badges are backwards and chaos reigns once more. It's long been a frustration of many who wear badges - the rectangular plastic kind that mig...