I took a remedial math class in college about 10 years ago, and have never forgotten this question that appeared on my final exam that has stumped just about everyone I have asked. Any help would be greatly appreciated…
Take a Rubik’s Cube and paint the outside of it red
Now take the cube apart so you have all the smaller cubes that make up the large cube.
How many of those cubes have:
one side red
two sides red
three sides red
no red sides
It sounds simple, but without having an actual Rubik’s Cube in front of you it is a very very difficult question. Being a dolt in math to begin with, I thought this was a rather unfair question to ask in a remedial math class, be it college or not.
one side red = 6
two sides red = 12
three sides red = 8
no sides red = theoretically 1 (the center cube) but actually none (rubik’s cubes don’t have a center cube)
Helps that I took my cube apart a lot more than I ever tried solving it by turning it…
Well, a Rubik’s Cube isn’t really 27 cubes all stuffed together* (3x3x3=27), but for the purposes of the problem I can see why it was used. I’ll go with that model, though: stack 27 small cubes into a 3x3x3 “supercube” and paint all exterior faces red.[ul][li]Zero Red Faces - 1 - only the one cube in the very center has no exterior faces[]One Red Face - 6 - the cube in the center of each face[]Two Red Faces - 12 - the cube in the center of each edge. Four on the top face, four on the bottom face, and one on each of the four vertical edges.Three Red Faces - 8 - each corner cube.[/ul]Does that add up? 1 + 6 + 12 + 8 = 27, which is the correct number.[/li]
If you’ve ever taken one apart you know what I mean. The “cubes” in the center of each face are all just plates, really, mounted by posts to a swivel in the center. The corner and center-edge cubes are held into the whole mess by small tabs that catch under the face-centers.
>> If you’ve ever taken one apart you know what I mean. The “cubes” in the center of each face are all just plates, really, mounted by posts to a swivel in the center. The corner and center-edge cubes are held into the whole mess by small tabs that catch under the face-centers. <<
I haven’t seen one of these devilish devices since about 1981, but as I recall it had six colors with nine faces per side. Doesn’t that equate to 36 outside faces? Damn, I have my shoes off, but I still don’t have enough fingers and toes to do the math here.
Yes, there are 54 outside faces. However, most of the cubes have more than one outside face, so there are fewer than 54 cubes. As has already been pointed out, there are 3[sup]3[/sup] = 27 cubes.
Zero Red Faces - 1 - the centre cube (if there is one)
One Red Face - 26; the question didn’t specify only one red face, so the cubes with one, two or three red faces are included (6of1 + 12of2 + 8of3)
Two Red Faces - 20 the question didn’t specify only two red face, so the cubes with two or three red faces are included(12of2 + 8of3)
Three Red Faces - 8
(Thank you, “I Got Six” (Schoolhouse Rock))