Many believe that a time travel would solve many problems, but in truth, it is more likely to cause them. In this brief riddle published by TED-Ed, exactly that happens: a professor accidentally crosses a portal that sends him to prehistory, and his assistant must rescue him by obeying a set of very specific conditions, combining nodes, quantum entanglement, and a mathematical theory in the background. Can you help?
The Riddle
The riddle presents Professor Ramsey, too focused and distracted at the same time, ending up headfirst in a temporal portal that sends him to prehistory. His assistant wants to react quickly and go to the rescue, but the problem is in the very nature of the portal: crossing it will automatically close, and she must carry the materials to create another.
- The portal to return to the laboratory requires at least three nodes that automatically connect to each other, forming a triangle. The color of those connections can be red or blue.
- The only way to generate a stable portal back to the present is that the triangle has all its sides the same color, either blue or red.
- Unfortunately, the colors are defined randomly, and there is no way to change the color once established.
- Fortunately, there is an advantage: connections between nodes can cross without any issues.
- However, the triangle must be composed of a node at each corner. Triangles formed by floating intersections don't count.
- As if that weren't enough, the assistant must work with the lowest possible number of nodes, or the portal will become unstable.
The question is: How many nodes must Professor Ramsey's assistant bring to the past to guarantee the formation of a triangular portal with all its sides blue or red?
(Editor's note: The video has Spanish subtitles)
Solving the Time Travel Riddle
The riddle is based on the so-called Ramsey theory, developed by mathematician and philosopher Frank Plumpton Ramsey at the beginning of the 20th century. The theory can be summarized as: "How large must a structure be to guarantee that a particular property remains intact?" In this case, we need a triangle with all sides blue or red, using the smallest number of nodes.
The video does a brief brute-force exploration: With 3, 4, or 5 nodes, there is a possibility of an incomplete pattern that could leave our unexpected travelers trapped in the past. However, the answer comes with the use of six nodes. Regardless of the initial configuration, with six nodes there will always be a blue or red triangle that will function as a return portal.
