I wear t-shirts a lot. A lot of them feature geeky topics. They’re are fun because they start conversations among the people I hang out with. The best times are when someone can take the geeky idea, and one-up it with yet another layer of geekiness.

For example, I have a shirt with this melting Rubik’s cube on it:

As geeky as this image is, I add to it by pointing out that even before the melting began, this isn’t a possible configuration of a Rubik’s cube. To avoid spoilers, I’ll explain why at the end of this post.

Here’s another shirt from my closet:

In this case, other people added to the geekiness of this shirt. One person suggested that the shirt is simply missing some punctuation, and it should say:

My password is “the last 8 digits of pi”

Of course, there’s still the problem of “pi” vs “π”...

Another person suggested that although no one knows the last 8 digits of pi, my security has been compromised, because it’s really easy to brute-force an 8-digit password, no matter what the digits are.

OK, back to the Rubik’s cube question: why is the melted cube not a real cube? Consider a solved Rubik’s cube:

Look at the the two faces colored orange and yellow. They meet at one edge, so there are only two corner cubies (the smaller cubes that make up the complete cube) that have both an orange and a yellow face.

Now think about the two orange-yellow corner cubies on a real cube. If you look at the corner, and think about the faces in clockwise order, one of the cubies must go orange then yellow, and the other must go yellow then orange. They have to have opposite handedness, if you will.

If you look at the melted cube, you can see two corner cubies with both orange and yellow, they are the two closest to the viewer. But they have the same handedness! Going around clockwise, they both go orange and then yellow. So this can’t be a real Rubik’s cube, because these two must be the only two orange-yellow corner cubies, and these two aren’t right.