The general Idea
I have an idea:
We now have many easily accessible computer programs that can easily search the shortest algorithms for a certain position. (May it be a ZBLL, OLL-CP or something else. It doesn't matter). However the shortest is not always the best. Often people then search...
a random thought that came across my mind today:
(nearly) all methods with steps work by reducing the cube group to smaller and smaller subgroups until only identity (=solved cube) is left. (between the steps the subgroup may be left again. however that is not of our interest in this topic.)
the question i will discuss here is the following:
for a (random) given permutation A, does there exist a permutation B with B A B'=A' (which is equivalent to B A B' A= id)? or in other words: can you invert any permutation by conjugation?
i start by discussing the problem in the symmetric group...
so every finite group (with less than n+1 elements) is isomorphic to a subgroup of the symmetric group Sn. (http://en.wikipedia.org/wiki/Cayley%27s_theorem)
however we dont need n to be ~10^18 to find the cube group as a subgroup in it.
my current upper and lower bounds for n are:
just wanted to inform (or remind) you of the upcoming transit of venus on 5th and 6th of june. its the last one until 2117 so take your last chance and observe this special phenomenon!
further information on wikipedia: http://en.wikipedia.org/wiki/Transit_of_Venus,_2012
i will try to make...
we just talked about this in university and i was curious about normal subgroups on 3x3.
i found a few obvious ones so far:
identity, whole group (haha)
edge flips, corner twists
edge permutations, corner permutations
(and of course you can link the ones that are disjunct and get a new...
U´ F U´ F2 U´B´ L D L´ B´ R´ F2 D2 F2 U´ R2 U D2 F2 D B2
z2 D2 R´ F D (4)
y´ U R´ U R U2 R´ U R (8)
U R´ U R U2 y R U R´ (7)
U2 RUR´U´R´FRF´ (9)
(UUUU) R´U2RUR´ z R2UR´DRU´ R2 (16)
47 moves = 6.1457tps
14.06 reconstruction: (starts at 1:56)
scramble: R2 U2 F2 L F2 D2 L' R' B L U R' B' D2 R D' R D B2 F
cross: z2 R2 y U' R2 z U2
F2L1: U' R2 U R U' R' U
F2L2: z' U' R U2 R' U' y R' U' R
F2L3: U R U' R' U2 z x U' R' U
F2L4: R' U R U' R U R' U'
59 moves, 4.2 tps :D
title says it all.
you are allowed to do rotations/AUFs in between. (otherwise it would make not much sense)
i was not even able to find an approach for this problem. i hope you come up with some solutions :D
additional (easier?) problem: we do not use only PLLs but all possible states...
just for fun... i think i can do sub18 of 12 easily. but its not that impressive if you count all the skips^^
times: (13.44), 20.97, 16.00, 15.19, 19.14+, 20.27, (DNF(20.78)), 20.33, 17.73, 22.38, 20.74, 14.42
(first 5 are 16.78 of 5)
EO: FsexyF' and wide sune
CO: all the algs...
scramble: D' L2 B2 L D L' U' B U2 D B2 U2 R2 U2 F B2 D B2 D' U' B' L' R D2 L'
xcross: z2 y' R U' R' r U2 R' z' x' U R2
pair2: U2 y R' U R
pair3: U' R U R' z' r U' z U' R
pair4: U' R U' R'
OLL: U' r y R U R' U' x' U'
PLL: R' U' R U' R' U' R' U' R U R U2
42 moves/9.67 secs= 4.3 tps