Thursday 14 June 2018

I wear t- a lot. A lot of them feature 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.

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