You’re overseeing the delivery  of crucial supplies to a rebel base deep in the heart of enemy territory. To get past Imperial customs, all packages must follow a strict protocol: if a box is marked with  an even number on the bottom, it must be sealed with a red top. The boxes are already being loaded  onto the transport when you receive an urgent message. One of the four boxes  was sealed incorrectly, but they lost track of which one. All the boxes are still  on the conveyor belt. Two are facing down:  one marked with a four, and one with a seven. The other two are facing up: one with a black top, another with a red one. You know that any violation  of the protocol will get the entire shipment confiscated and put your allies in grave danger. But any boxes you pull off for inspection won’t make it onto this delivery run, depriving the rebels  of critically needed supplies. The transport leaves in a few moments, with or without its cargo. Which box or boxes should you  grab off the conveyor belt? Pause the video now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 It may seem like you need to inspect  all four boxes to see what’s on the other side of each. But in fact, only two of them matter. Let’s look at the protocol again. All it says is that even-numbered boxes  must have a red top. It doesn’t say anything  about odd-numbered boxes, so we can just ignore  the box marked with a seven. What about the box with a red top? Don’t we need to check  that the number on the bottom is even? As it turns out, we don’t. The protocol says that  if a box has an even number, then it should have a red top. It doesn’t say that only boxes  with even numbers can have red tops, or that a box with a red top  must have an even number. The requirement  only goes in one direction. So we don’t need  to check the box with the red lid. We do, however,  need to check the one with the black lid, to make sure it wasn’t incorrectly  placed on an even-numbered box. If you initially assumed the rules  imply a symmetrical match between the number on the box  and the type of lid, you’re not alone. That error is so common, we even have a name for it: affirming the consequent, or the fallacy of the converse. This fallacy wrongly assumes that just because a certain condition  is necessary for a given result, it must also be sufficient for it. For instance, having an atmosphere  is a necessary condition for being a habitable planet. But this doesn’t mean that  it’s a sufficient condition – planets like Venus have atmospheres  but lack other criteria for habitability. If that still seems hard  to wrap your head around, let’s look at  a slightly different problem. Imagine the boxes contain groceries. You see one marked for shipment  to a steakhouse and one to a vegetarian restaurant. Then you see two more boxes  turned upside down: one labeled as containing meat, and another as containing onions. Which ones do you need to check? Well, it’s easy – make sure the meat isn’t being shipped  to the vegetarian restaurant, and that the box going there  doesn’t contain meat. The onions can go to either place, and the box bound for the steakhouse  can contain either product. Why does this scenario seem easier? Formally, it’s the same problem – two possible conditions for the top of the box, and two for the bottom. But in this case, they’re based on  familiar real-world needs, and we easily understand that  while vegetarians only eat vegetables, they’re not the only ones who do so. In the original problem, the rules seemed more arbitrary, and when they’re abstracted that way, the logical connections  become harder to see. In your case, you’ve managed  to get enough supplies through to enable the resistance  to fight another day. And you did it by thinking  outside the box – both sides of it.