A Puzzle

I was playing around with the Rubik’s cube at our house. With two math teachers in one apartment, there has to be at least one Rubik’s cube in the vicinity. It goes without saying.

I’m no Rubik’s expert or anything, but I can get the T’s (the top side all one color, with the first band around the edge in line and matching the middle square’s color for that face) without too much trouble. In fact, getting the T’s is the first step in every Rubik’s cheat sheet I’ve ever read and they don’t tell you how to get them. It’s that easy to figure out on your own, so no kudos to me for being able to get them.

Problem was, I could not for the life of me get the T’s!

I was playing around, and getting a little perplexed as to why I can’t do this, analyzing what I needed to move in order to make some progress when I realized that there were two pieces with red and white faces. Someone had switched the stickers. Looking closer at the cube, it’s clear that one of the white stickers has been peeled up (at least twice, since I switched the white from its former incorrect square to the one it’s currently on).

Alas, I have still been unable to get the d@mn T’s…

But as I’ve been messing around with it, I have realized that there is no way all of the stickers are in the correct places. There have been further switches which I have not yet found. Ones that are not as obvious, since so far as I’ve been able to determine, there are not any more duplicates. However, I can get cubes into the proper place, but with the two faces reversed. I don’t think you can switch the orientation of the faces successfully when the cube is in the proper placement. How do I know it’s in the proper placement? Because the middle squares can’t move…at least not without moving the stickers.

Avery told me to move the stickers back. Obviously I could just “solve” the cube and I’d know that the stickers were all in the right place, but that’s no fun.

I am curious as to what the minimum number of moves I’d need to make would be. Is there a way that I can figure out the number of swaps that the switcher made? Can I fix the cube with one switch? Will I need to make 10 switches? I have to admit, I find this puzzle more interesting than the original Rubik’s cube puzzle itself.



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