For info on speedcubing in general see the speedcubing.com main site.

I've been interested in big cubes (6x6x6 and larger) for a while now and my favorite so far is the 20x20x20. Some basic facts on the 20x20x20 cube, it's an even cube and follows the rules of all other even cubes. The number of combinations to a 20x20x20 cube is absolutely enormous. Below is an exact calculation of the number of possible combinations to a 20x20x20 cube.

This works out to about 1.3366106203729717328004388722211 * 10^1477 possible combinations. Click here for an idea of how large that number is. An interesting thing to note is that out of all the possible combinations on a 20x20x20 there is more than one "solved" state. This is due to the fact that if the centers are solved the pieces on that face can be in many different combinations and the face still appears solved. Below is the exact calculation of the number of solved states,

That's about 2.5074588992487256829778381899096 * 10^646 solved states! So for the 20x20x20 cube there is only one possible state where every face is a solid color, however practically when solving the cube you can piece that state together in the above number of ways. This is similar to having the center pieces on a 3x3x3 rotated while the cube is solved. The cube will still be solved with ever face a solid color, however the centers can rotate into 2048 different states without you ever knowing they were rotated! If you're interested in the number of combinations to different sizes of cubes where the position of every center piece is noticeable, called the n x n x n supercube, then check out my formula page for some formulas I came up for the number of combinations to different types of cube related puzzles. A supercube would be a cube that has a picture on every face, with the pictures designed like a jigsaw puzzle. In order to solve the cube, every center piece on the entire cube must be returned to its original position. This leaves exactly 1 solution out of many more possible combinations than the normal n x n x n cube.

I recently solved it and took screen captures throughout my solution and here you can watch how exactly a 20x20x20 cube is solved, or at least one possible way (there are many ways to solve rubik-like puzzles). My solution to the 20x20x20, and in fact

So if you're ready click on start to see how its done

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