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  • 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.

You're overseeing the delivery of crucial supplies to a rebel base

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B1 US TED-Ed protocol marked numbered steakhouse conveyor belt

Can you solve the rebel supplies riddle? - Alex Gendler

  • 101 7
    ally.chang posted on 2020/02/11
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