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#### 你能解开时间旅行谜题吗？

Can you solve the time travel riddle? - Dan Finkel

Your internship in Professor Ramsey’sphysics lab has been amazing.

Until, that is, the professor accidentallystepped 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 individualconnection manifests at random,

and there’s no way to chooseor 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.

What’s the minimum number of nodulesyou 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 entirebranch of mathematics

known as Ramsey Theory developed from it.

Ramsey Theory is home to somefamously 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 ofconnections

that avoids creatinga 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 connectto 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 noduleson 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 connectionswould 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 theconnections 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 wouldgive you valuable life experience.

Turns out, that didn’t take much time.