Friendly Robot Overlord

My 4x4 Rubik's cube died the other week, so in my sadness I decided to make a new typeface by using my 5x5 cube. I put some paper on my desk to give a mostly white background, and then spelt out every upper case letter on the 5x5 cube. I took 2 high resolution photos of each (with the camera on a tripod and the cube in a mostly consistent spot) and then selected one of the images, resized it, stitched it with all the other images, edited out the desk and increased the brightness and saturation to bring you this:

(note that I stuffed up when I did the resizing and accidentally saved the resulting images as jpegs, so there is some dodgy artifacts there which are then made even more obvious when I increased the brightness and saturation, then to save bandwidth I did another round of jpeg compression at the end just for a laugh. There is a png file with the same name as the jpeg if you want slightly better quality, email me if you want the higher-quality source images.)

In pleasant news, since it was recently my birthday, I now have a new 4x4 cube, which has inspired me to go back to my search for a method to fix the "parity error". For the non-Rubik's cube people, when you have a normal 3x3 Rubik's cube, there are actually multiple solutions since the centre square on each face can be rotated differently. This isn't very obvious, because they are just blocks of solid colour, so they don't seem to face a particular direction. But if you get one of those stupid sudokube's then it is much more obvious - you can get all the numbers in the right spots, but have some of the 5's upside down or whatever. But even though there are 6 faces where each could be facing 4 ways there aren't 24 different solutions, because a lot of these combinations are impossible. I don't know enough about group theory to be able to be certain about this, but I'm pretty sure that rotating a single face somewhere means that you will rotate one of the other faces (this is talking about the final solved state of the cube - you can easily rotate a face without moving others, but that will mess up the colours). So I'd guess that there are 12 different solutions (even though they all appear identical).

With a 4x4 cube, you can think of it as a 3x3 cube, but where the middle face is split up into 4 and the edge pieces are split up into 2. So to solve it, you will have to get the 4 parts to each face back together, and the 2 parts to each edge together as well. However there are multiple ways you can reconstruct each edge and each face - even though they look identical, it is possible that you are reconstructing it in a way that means you have one of the edge pieces flipped. So you can think you have solved it, and do your thing, but then you get to the very end, and you have 2 edge pieces (corresponding to a single edge in the 3x3 cube) which are flipped. This is the parity issue, and to fix it, you can either find a website which gives you a sequence of moves you can memorize (boring), scramble it up and try again (50% chance of success) or try to figure out how to fix it properly. In the past I've used the scramble method, but now I feel like working out a method for fixing it with 100% chance of success.

In other Rubik's cube news, I figured out my own algorithm for solving 3x3 cubes, and that was a few years ago, and while I don't play with a rubik's cube every day, I would say that I thought I had done it enough to have encountered every situation. But last night when playing with a 3x3, I got into a situation where there was a hole in my algorithm (i.e. a situation I'd never seen before). It was easy to fix, but it still surprised me a lot.