TED-Ed Video Lesson Transcript:
The discovery of an alien monolith on planet RH-1729 has scientists across the world racing to unlock its mysteries. Your engineering team has developed an elegant probe to study it.
The probe is a collection of 27 cube modules capable of running all the scientific tests necessary to analyze the monolith. The modules can self-assemble into a large 3x3x3 cube, with each individual module placed anywhere in the cube, and at any orientation.
It can also break itself apart and reassemble into any other orientation.
Now comes your job. The probe will need a special protective coating for each of the extreme environments it passes through.
The red coating will seal it against the cold of deep space, the purple coating will protect it from the intense heat as it enters the atmosphere of RH-1729, and the green coating will shield it from the alien planet’s electric storms.
You can apply the coatings to each of the faces of all 27 of the cubic modules in any way you like, but each face can only take a single color coating. You need to figure out how you can apply the colors so the cubes can re-assemble themselves to show only red, then purple, then green.
How can you apply the colored coatings to the 27 cubes so the probe will be able to make the trip?
Pause here if you want to figure it out yourself.
You can start by painting the outside of the complete cube red, since you’ll need that regardless.
Then you can break it into 27 pieces, and look at what you have. There are 8 corner cubes, which each have three red faces, 12 edge cubes, which have two red faces, 6 face cubes, which have 1 red face, and a single center cube, which has no red faces.
You’ve painted a total of 54 faces red at this point, so you’ll need the same number of faces for the green and purple cubes, too.
When you’re done, you’ll have painted 54 faces red, 54 faces green, and 54 faces purple. That’s 162 faces, which is precisely how many the cubes have in total.