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  • Your internship in Professor Ramsey's physics lab has been amazing.

  • Until, that is, the professor accidentally stepped through a time portal.

  • You've got just a minute to jump through the portal to save him before it closes

  • and leaves him stranded in history.

  • Once you're through it, the portal will close,

  • and your only way back will be to create a new one

  • using the chrono-nodules from your lab.

  • Activated nodules connect to each other

  • via red or blue tachyon entanglement.

  • Activate more nodules and they'll connect

  • to all other nodules in the area.

  • As soon as a red or blue triangle is created with a nodule at each point,

  • it opens a doorway through time that will take you back to the present.

  • But the color of each individual connection manifests at random,

  • and there's no way to choose or change its color.

  • And there's one more problem:

  • each individual nodule creates a temporal instability

  • that raises the chances the portal might collapse as you go through it.

  • So the fewer you bring, the better.

  • The portal's about to close.

  • What's the minimum number of nodules you need to bring

  • to be certain you'll create a red or blue triangle and get back to the present?

  • Pause here if you want to figure it out for yourself!

  • Answer in: 3

  • Answer in: 2

  • Answer in: 1

  • This question is so rich that an entire branch of mathematics

  • known as Ramsey Theory developed from it.

  • Ramsey Theory is home to some famously difficult problems.

  • This one isn't easy, but it can be handled

  • if you approach it systematically.

  • Imagine you brought just three nodules.

  • Would that be enough? No - for example, you might have two blue

  • and one red connection, and be stuck in the past forever.

  • Would four nodules be enough? No - there are many arrangements here

  • that don't give a blue or red triangle.

  • What about five?

  • It turns out there is an arrangement of connections

  • that avoids creating a blue or red triangle.

  • These smaller triangles don't count because they don't have a nodule at each corner.

  • However, six nodules will always create a blue triangle or a red triangle.

  • Here's how we can prove that without sorting through every possible case.

  • Imagine activating the sixth nodule,

  • and consider how it might connect to the other five.

  • It could do so in one of six ways:

  • with five red connections, five blue connections, or some mix of red and blue.

  • Notice that every possibility has at least three connections of the same color

  • coming from this nodule.

  • Let's look at just the nodules on the other end

  • of those same three color connections.

  • If the connections were blue,

  • then any additional blue connection between those three would give us a blue triangle.

  • So the only way we could get in trouble

  • is if all the connections between them were red.

  • But those three red connections would give us a red triangle.

  • No matter what happens, we'll get a red or a blue triangle,

  • and open our doorway.

  • On the other hand,

  • if the original three connections were all red instead of blue,

  • the same argument still works, with all the colors flipped.

  • In other words, no matter how the connections are colored,

  • six nodules will always create a red or blue triangle and a doorway leading home.

  • So you grab six nodules and jump through the portal.

  • You were hoping your internship would give you valuable life experience.

  • Turns out, that didn't take much time.

Your internship in Professor Ramsey's physics lab has been amazing.

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B1 US TED-Ed triangle portal ramsey doorway internship

Can you solve the time travel riddle? - Dan Finkel

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    ally.chang posted on 2020/02/05
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