Permutations Permutations are a one to one correspondence of a set unto itself or a set that is arranged into a particular order. The number of permutations in a set can be counted. Counting these permutations can be easy if you have a small number of elements that only have one orientation. An example of this is if you have only three elements with one orientation then there would be 3! (Factorial) which is 3*2*1= 6 with the operation * being multiplication. If you take elements that have more than one orientation counting the permutations becomes exponential as the other orientations have to be counted also. If we take three elements with 2 orientations then we still have 3! but we have 3 elements with two orientations that will give …show more content…
The operation between the 3! and 2^3 is also multiplication so the total permutations are 3!*2^3=48. The Rubik’s Cube has 26 cubes which by itself would be 26! although we need to take the cubes by their type. The first and easiest to compute is the center pieces because they only have one orientation. There are 6 center pieces although they do not move so they have 1!=1 and then we would have 1*1*1*1*1*1=1. There are the eight corner pieces that have three orientations per corner piece which will give 8!*3^8. Next we have the 12 edge pieces each with two orientations each. This will give 12!*2^12. We can put these together for the total number of permutations although this assumes that the cube is taken apart which is not the case. Because the cube is put together and is limited by the movements available only 1 of 12 positions are possible. Therefor we have to divide the total by 12 which gives (8!*3^8)*(12!*2^12)/12 which is over 43 quintillion …show more content…
You must match a front face with a yellow left corner as shown. Execute the following R-U-Ri-U-R-U-Uri

** Do this sequence 1,2,or 3 times to achieve a complete yellow top(U) Face. After each sequence execution you must re-orient the cube to rematch one of the states is step 2. Keep repeating until all corners are yellow.

Step 6: Reposition the four corners to the correct location and proper orientation. Cube reference position: While holding the cube with the yellow face up twist the top (U) face until at least 2 corners are in the correct location. Starting from the top left corner going CW label the 4 corners A-B-C-D. The 2 correct corners must be in positions A-B or A-D or B-C. In the picture corners A-D are in the correct position. Execute the following: Ri-F-Ri-B-B-R-Fi-Ri-B-B-R-R-Ui.

Now reposition the cube so the 2 corners A-B are two back corners and execute again. In some cases this will completely solve the cube. In the case where all corners are in the correct location but the edge pieces are not you will move on to Step