From cube-lovers-errors@mc.lcs.mit.edu Thu Sep 17 17:18:28 1998
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Date: Mon, 14 Sep 1998 14:14:22 -0400 (Eastern Daylight Time)
From: Jerry Bryan
Subject: Re: Weak Local Maxima, 6f from Start
In-Reply-To: <14Sep1998.111621.Hoey@AIC.NRL.Navy.Mil>
To: Cube Lovers
Message-Id:
> It turns out that 6f is indeed the shortest. There are two such positions
> unique to symmetry which are 6f from Start, the Pons and one other. The
> other one is quite pretty:
>
> L2 R2 D2 U2 B' F (6f*)
>
I didn't notice it originally, but this position is in the slice
subgroup, and is only one slice move from Pons. Half turns such
as L2 can be written equally well as either LL or as L'L',
so we can write (L2 R2) as (L'R)(L'R) and (D2 U2) as (D'U)(D'U).
Thus, the weak local maximum 6f from Start can be written as five
slices, one slice short of Pons.
L'R L'R D'U D'U B'F
All we would have to do to get the Pons would be to add one more
B'F slice.
----------------------
Jerry Bryan
jbryan@pstcc.cc.tn.us