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.

Get the solution to the bonus riddle here: https://brilliant.org/TedEdTimeTravel/! Also, the first 833 of you who sign up for a PREMIUM subscription will get 20% off the annual fee. Riddle on, riddlers!

According the ministry of Vulcan science, time travel is not possible.

No wonder why professor is named Ramsey

This question is about finding R(3,3) the Ramsey number

Answer for bonus.

Since we know there's at least one triangle, I'll call its points A,B, and C and assume it as red.(we can swap the color later)

Now let's think about point D's connections to A,B, and C.

If at least 2 red connections are made, there will be another red triangle.

So D has at least 2 blue connections to A B C.

This is also true for point E and F.

If there is at least 1 blue connection between D E F, there will be a blue triangle.

But if there isn't any blue connection, it means it is a red triangle.

vice versa for another color.

6666666666666666666666666

WHERE'S THE LAMB NODULEFor anyone wondering the ansure to the bonus rittel is…

Yes, Pick any vertex zz. It connects to five other vertices, and so at least three of the edges coming from it must be of the same colour. Suppose, for definiteness, that three vertices z_1,z_2,z_3z1,z2,z3 are connected to zz with red edges. If any two of these vertices, say z_izi and z_jzj, are connected by a red edge, then z,z_i,z_jz,zi,zj is a red triangle. Thus no two of these vertices are connected by a red edge, and hence z_1,z_2,z_3z1,z2,z3 is a blue triangle. Thus at least one monochromatic triangle exists.

However we have found them, suppose that the vertices w_1,w_2,w_3w1,w2,w3 are connected by a monochromatic triangle. For definiteness, suppose that this triangle is red. Suppose that there are no other red triangles. If u_1,u_2,u_3u1,u2,u3 are the other three vertices, then two of them must be connected by a blue edge (otherwise we would get a new second red triangle). Suppose that the edge u_1u_2u1u2 is blue. If any two of the edges connecting u_1u1 to v_1,v_2,v_3v1,v2,v3 were red, say u_1v_iu1viand u_1v_ju1vj, then u_1,v_i,v_ju1,vi,vj would be the vertices of a red triangle. Thus at least two of the edges u_1v_1,u_1v_2,u_1v_3u1v1,u1v2,u1v3 must be blue. Similarly, at least two of the vertices u_2v_1,u_2v_2,u_2v_3u2v1,u2v2,u2v3 must be blue. Consequently there must be some 1 le k le 31≤k≤3 such that u_1v_k,u_2v_ku1vk,u2vk are both blue, and hence u_1,u_2,v_ku1,u2,vk are the vertices of a blue triangle. Thus we have found a blue triangle.

Thus there are always at least two monochromatic triangles.

TED-Ed: The portal's about to close.

But you have enough time to explain how to solve this riddle which took about 3 minutes…

But we jumped through the same portal as the professor 3:56

Or you could think of it the simple way because if you have six no mater what that’s at least 3 and 3 making it a for sure triangle no matter what…

Plot twist: Ramsay accidentally walked into a dinosaurs mouth and you are teleported in a dinosaurs mouth

Can you solve th-

Me: no but I'll watch

0:12

Until, that is, he called you a donkey and said the meat is undercooked!

We called Dirichlet principle

that weird guy keeps slapping the computer, not typing.

00:11 HER HAND… BIG!!

bring the box, then keep throwing 3 at a time!!

The only Ted-Ed puzzle I solved, within 10 seconds 😏😌😱

Then how did the scientist get through with only 3 at the beginning of the video?

Just throw the whole damn box in and make the professor do the damn work of going back

0:20 YO this scene is GORGEOUS!

May not be true in all cases but I did 0.5 (50% Red / 50% Blue) and multiplied by the number of modules at 5 I had 2.5 minimum connections and at 6 I had 3…. so I concluded six, I wonder if it'd work for others

I guessed six with no logic reasoning whatsoever

Is this where the infinity stones came from

The bonus riddle’s answer is yes

However, the question doesn't say that the nodules have to be on the same plane. Therefore, using 5 nodules to create two tetrahedrons will do the job.

I can't believe that I actually got this one right i just said it was 6 because logically if you think of it like proportions if you bring 3 3=300 as a total and there is a 50 % chance of a red or blue on each of the balls so it would be 150 over 300 which is only half if you do that times 2 your bound to have a triangle no matter what

I actually did this one

Yes I just guest I'm a brilliant scientist yay like if you got it right as well 👍

I want to know more about this type of mathematics. Anyone have any recommendations?

I want to know more about this type of mathematics. Anyone have any recommendations?

You just need 4 stones??

Who wanna get more riddles like here????

I think that 6 Nodules can make only 1 people through cuz there's only 1 triangle made by 6 nodules.

If u also think like me, leave a like! 😉

Bonus: Only 3 nodules in those 6 make a portal.

Take the box with you and decide after going there.Trial and Error method

Ted ed should remove can you solve in their title just the time travel riddle

well if a portal can only send one person then how would the other character go into the past

So turns out I almost got it right but i thought that since the dude who got last had three already (since he used it to travel ) I only had to bring three instead of 6

omg i solve it yay

Can't I just take the entire box and jump through the portal? The professor is clearly much smarter than me,so I'll just let him solve it. Or even better,I could throw the box through the portal and I wouldn't have to risk getting trapped 60 million years into the past.

So if its 2 people on the past/future and if you and your boss want to get home you need 6 chrono-nodules but only 1 person will enter the portal…

then… 2 x 6 = 12 chrono-nodules = 6 chrono-nodules for both, yeah easy

When it does five red or blue connections, and the remaining ones are different from the five, no triangles would be formed.

Waiting for an answer…

I don't jump in the portal to save the scientist in the first place

boomIf he portal was still open when the scientist was inside, couldn’t he just go back through??

Isn't it 5 if you connect a triangle and 2 are red and one is blue you get rid of the blue one and place another one if that is blue than you get rid of that one and if it another blue you just use the blues for their own portal

Oh I thought the thumbnail was tits not glases man :/ 😂

Can't i just grab a whole bunch and keep trying with 3s until it works?

Bonus riddle? If I were the intern I would go through the portal asap

Ted ed is full of interesting accidents

What about 5 nodules, with the fifth one at the intersection point of the diagonals of the quadrilateral formed between the other four ?

I think it works fine, if there is no rule against colinear nodules ( 3 nos )

Bold of you to assume that I'm helping this guy outForgive me, but… wouldn’t you just need for nodules? If you put them in a kite figuration- similar the configuration in the example of the solution, only with the two nodes adjacent to the lover tail missing- wouldn’t that be enough?

I got this😀😀😀

get every nodule try triangles untill you succeed try again go back in time baby 😀

GORDON RAMSAY IS THAT YOU

the video shows that the thingies just fall when they get teleported through…why not just pick em back up and create another portal?

Yeah, I grabbed six nodules but after the video ended, 1 minute has already passed by, so THANKS TED-ED.

Answer should be 4 .

A pyramid can be formed with every nodule having 3 connections

i kind of guess it randomly i thought it's either 3 or 6 lol i feel smart now nice

can't you bring a lot of nodules and keep making triangles until you strike gold

WARNING.

spoilers down there.

Cross at your own risk.

Yay, I actually got it right.. 😬

why cant she take more just in case?

Omg six infinity stones but theyre all time stones. Can thanos still kill half the universe

New theory: you take the whole box and throw down the nodules until you make a portal

Why do you have to take a minimum amount anyway why dont you just take the whole box with you

2nd riddle answer: throw 6 nodes into the portal and not go through yourself

When I heard that the professor’s name was “Ramsey”, it made me think, ‘Huh, that reminds me of Ramsey Theory.” Little did I know, that was the answer! Arggh, darn it!

i guessed five im mad. >:(

I guessed, and I was right. That my friends is called survival instincts.

I got it

Bring as many as you can and keep forming triangular portals.

EEAASSSYYY

It’s Ramsay not Ramsey!

So many people are saying omg i guessed 6 and its correct (i'm one of those)but i did had a logic

i guessed 6 in a hexagon before being told the fact that you cant choose the red or blue ones and i ended up being right lol

Easier explanation: With six nodules, each one needs to connect to five others, which means at least three will be in the same color. Now let's take one nodule and look at the end nodules of its three connections of the same color. These three nodules also need to be connected to each other, and if one of these connections is of the previous color, it will be a triangle with the starting nodule. If none of them are, they will all be of the same color, hence they will then form a triangle.

I would go back in time to when before I finished my chicken wings

bonus riddle is wrong bc you went in after him

Think 3D and the correct answer will be a minimum number of 4. Yes 6 is correct when we think 2 dimensional, but who says the nodules must all be on a flat surface? You CAN think 3D. Just put 3 nodules down on the ground shaped like a triangle. Hold the fourth nodule exactly on top of the triangle’s center above the ground. You now have a pyramid with 3 triangles in the air and one triangle on the ground. Now out of 4 triangles, you will always have at least one all-blue or all-red triangle.

This is good sense

You put 6 nodules

Portal opens

You get in completely

Unfortunately for you, you accidentally put tomato sauce on 1 of the blue nodules

Your stuck in between the space time continum

How unlucky you are

E

Either throw the box to the scientist or you jump through the portal with the whole box and start with three nodules and add one more each time till it works

Me: five sounds nice-No 6, 3 for 2 triangles.

Ted-ed: the answer is 6

Me: yes big brain time

fyi it's RamsAy !

3:38

Just grab him through, you have long enough arms

Just bring the entire box smh.

The animation is cute

"What's the minimum number of nodules you'll need to bring to guarantee you create a fully red or blue triangle?"

Me: Well, Prof., it was nice knowin' ya.

*take

what the minimun number you need to TAKE

m r r a m s e yWhy not just make another time portal with 3 nodes before you even go through the portal, then deactivate the time nodes, and go through the portal to save the professor with those same 3 nodes? Then if the portal fauls, why not just make more portals to save him, after you find which nodes you need.

I said six I win nice!

You bring a lot of them but only use them one at a time until a portal opens. You could get lucky and only have to activate as few as three.

My guess was right

Five. A square with one in the middle

What if you got all red or blue entanglements?

We need a game with this art style

To be completely honest I got it perfectly correct on my first try my logic was if there's two colors of lasers then if I bring twice the amount of lasers necessary then with the 50/50 split their there should be a more than even odds that a red or blue triangle would form

Me an intellectaul: I'll just take the whole box and keep on throwing some until I get a triangle because they only cause instability once used

Couldn’t you just bring 12, give 6 to the guy who fell in, make your own portal and then have him make one once you leave?