Moves HTM QTM
0 1 1
1 11 8
2 90 51
3 717 306
4 5315 1722
5 36372 9288
6 226396 47915
7 1202923 227469
8 4243588 945926
9 4886281 2942196
10 420636 4862890
11 150 2659285
12 385150
13 2501
So basically, is parity caused by non fixed centers or just by number of layers?
A sample HTM antipode: F R F2 U' R F R' F' R2 F2 w
A sample QTM antipode: F R U' w U' R F' R w' U2 F' U'
Not sure if new, but I came up with a neat way to simulate.
Represent the state as a string like
"UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"
which for those 20 pieces tell their current location. If we do a U turn, we get:
"UL UF UR UB DF DR DB DL FR FL BR BL ULF UFR URB UBL DRF DFL DLB DBR"
This says the first piece (UF) is now at UL, etc.
This can be implemented by changing exactly those locations having the turn name (U)
"UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"
and cycling all other characters in that cubie location ("U" cycles F->L->B->R->F):
"UL UF UR UB DF DR DB DL FR FL BR BL ULF UFR URB UBL DRF DFL DLB DBR"
So a state is given as such a string, and moves are defined by for example "U"=>"FLBR". It's really easy and natural to implement, no ugly numbers, which is why I find it neat. Could also be used for Megaminx and Pyraminx, for example (edit: darn, I just realized there aren't many people face-turning the pyraminx ).
Chris, would that mean that the scramble
U' F2 U F2 U' B2 F2 L2 D' L2 D' L' R U' B' U2 F2 D B' F2 D2 (normal turns)
would have the solution
U F2 U' F2 U B2 F2 L2 D L2 D L R' U B U2 F2 D' B F2 D2 (your kind of turns)
?
I don't know why this is the case, it's not intuitively obvious to me. This is interesting! I'll try looking at other scrambles to see this relationship and figure out why it is (I feel like you already have).
A 4-twist on 3x3x3: r U2 R' U2 y' R2 D2 r U' r' D2 r' U' L U l2' U'
I personally find the concept of inspection weird.
Holding inspection and non inspection events seems a bit cumbersome.
What procedure would you use for no-inspection?
Same as BLD, you remove the cover thyself.
We would need a standard cover so that all competitors use covers of the same shape/dimensions and weight no matter where they compete.