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Solving Rubik's cube in 36 quarter turns
Submitted by silviu on Sat, 01/14/2006 - 12:44.In this paper we present a method of solving Rubik's cube in 36 quarter turns. The proof have many common facts with other methods presented on the forum. In able to prove our claim we have used the corner and edge permutation analysis done for the first time by Bruce Norskog.
We call the group of corner edge permutations of the cube for CEP and cube group for C. Let N be the normal subgroup that fixes cubies. Then we have a homomorphism hom:C->C/N=CEP such that hom(g)="permtutation of cubies done by g". Let a be the unique antipode in CEP. Every element in CEP can be written as x*a. Where x is an element requiring at most 18 quarter turns according to Norskog's analysis. There are 220 elements at distance 17 and 1 element at distance 18. So we could say that all elements of CEP except 220+1 elements can be written as x'*a where x' is an element requiring at most 16 quarter turns.
We call the group of corner edge permutations of the cube for CEP and cube group for C. Let N be the normal subgroup that fixes cubies. Then we have a homomorphism hom:C->C/N=CEP such that hom(g)="permtutation of cubies done by g". Let a be the unique antipode in CEP. Every element in CEP can be written as x*a. Where x is an element requiring at most 18 quarter turns according to Norskog's analysis. There are 220 elements at distance 17 and 1 element at distance 18. So we could say that all elements of CEP except 220+1 elements can be written as x'*a where x' is an element requiring at most 16 quarter turns.
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