Notes for Thurs Feb 24
* Rubik "twistiness" and "turniness" as conservation laws
* final version of number of positions, 3x3x3
- other sizes?
- 2x2x2
- 4x4x4
- 5x5x5
- other shapes?
* cubelets, various approaches to solving the thing
- layer by layer
- corners, then edges
- edges, then corners
- back 2 corners, back 5 edges, front 2 faces
- others
* subgroups:
* (RL') (UD') (FB') slice group
- number of positions?
- pretty patterns?
- ways to "solve" it?
* (R) (F) 2-side group
* corners only group
* edges only group
* operators to find:
* permute 3 corners, leave all edges and other corners alone
* permute 3 edges, leave all corners and other edges alone
* twist 2 corners in opposite directions
- without worrying about edges
- leaving edges alone
* twist 2 edges in opposite directions
*
* Jim's method:
* edge's, via standard commutator and 3-cycle ignoring corners
* 2 out of place => odd number of moves => make one move
* 2 flipped => 2 commutators
* corners, via 3-cycles and rotate 2 in place
* One way to think about finding operators:
Let "A" = (bunch of moves that disturb only one cubie on a layer)
Let "B" = rotation of that layer
Then A B A' does something interesting...
* Testing your visualization of the Rubik's Cube:
have a friend make up to 3 moves. Can you undo those three
exactly? 4 moves? 5?? 6???
assign:
* Continue working on solving the cube, in any way you like.
See how many of the suggested algorithms you can find.
How many moves can you backtrack?
* How many positions are there in the (R) (F) generated 2-face group?
* See if you can come up with a step-by-step
written algorithm for getting back
to the solved position from any element, i.e.
First step: use the () operator which does () to get () pieces solved.
Second step: use the ...
* These kinds of solution techniques are
called "nested subgroups" method of solution. Why?