A TedEd by Dan Finkel
Imagine you are working as an intern for a professor. One day, he accidentally walks through a time portal. You have one minute to go through and bring him back before he is stuck forever. Once you go through, the portal will close. The portals are created by little chrono-nodules, which generate lines of either blue or red when conncted to other nodules. The colors are random, and a portal is created when a triangle of any one color is formed. The problem is that each extra nodule increases instability, heightening the chance it will close as you step through. How many should you take to be sure you will have a portal while minimizing the risk of it closing? It is easy to see that 3, 4, and 5 don't work. What about six? You don't actually need to work out each case. If you draw 5 lines from one nodule, there are six possible combinations. If you look at the cases, there is always three of each color. If the lines connecting those are the same color, you have a portal. But what if they aren't? Then those lines will form a triangle of the other color, insuring you always have a portal.
BONUS: What if the portal only allows one person before closing? Is six enough to ensure both of you get home?
Did you solve the bonus? Comment below!
