Can you solve the time travel riddle? – Dan Finkel

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.

100 Replies to “Can you solve the time travel riddle? – Dan Finkel

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

  2. 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.

  3. For 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_2u1​u2​ 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_iu1​vi​and u_1v_ju1​vj​, 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_3u1​v1​,u1​v2​,u1​v3​ must be blue. Similarly, at least two of the vertices u_2v_1,u_2v_2,u_2v_3u2​v1​,u2​v2​,u2​v3​ must be blue. Consequently there must be some 1 le k le 31≤k≤3 such that u_1v_k,u_2v_ku1​vk​,u2​vk​ 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.

  4. 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…

  5. 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…

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

  7. 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

  8. 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.

  9. 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

  10. 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! 😉

  11. 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

  12. 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.

  13. 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

  14. 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…

  15. 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

  16. 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 )

  17. Forgive 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?

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

  19. 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!

  20. 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

  21. 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.

  22. 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.

  23. 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


  24. 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

  25. "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.

  26. Why 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.

  27. 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.

  28. 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

  29. 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

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