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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!

• 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.

• 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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# Can you solve the time travel riddle? - Dan Finkel

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ally.chang posted on 2020/02/05
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