Thread: "MagicTile Solving intermediate report"

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MT_ell_sph_dode_E_0-1-0,11 part 2
b.PNG>

After succeeding with the cornerfaces I'm left with a single corner swap
!! I have macros to manage the edgefaces, small faces and central faces,
which do not touch the corners. How can I solve this parity problem ?
Because a belt of 10 corners is even I can go from 2134567890 to
0987654321with 3-cycles (even number of swaps; pay attention to the
reversed 21 in startposition). Then I have to swap the upper and lower
ring of 5 corners (5 swaps, odd). Then change direction in each 5-ring
(even number of swaps). Total : odd number of swaps which is not
possible with 3-cycles.
I don't see a solution for the moment.
Who can help me?


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_0-1-0,11_b.PNG">MT_ell_sph_dode_E_0-1-0,11 part 2 

After succeeding with the cornerfaces I'm left with a single corner s=
wap !! I have macros to manage the edgefaces, small faces and central f=
aces, which do not touch the corners. How can I solve this parity problem ?=

Because a belt of 10 corners is even I can go from 2134567890 to 09876=
54321with 3-cycles (even number of swaps; pay attention to the reversed 21 =
in startposition). Then I have to swap the upper and lower ring of 5 corner=
s (5 swaps, odd). Then change direction in each 5-ring (even number of swap=
s). Total : odd number of swaps which is not possible with 3-cycles.
I d=
on't see a solution for the moment.
Who can help me?

Ed,

You need to first swap the two incorrect 3c corners to fix them. Then you n=
eed to do two swaps for triangles in two orbits. Although you cannot do one=
swap in a single orbit, it turns out you can do two of them simultaneously=
: Let A and B be two adjacent edges sharing one vertex. (A,B)*3 does the jo=
bs. Please examine which two orbits this algorithm affects and apply it in =
the correct spot. Then you can use your old algorithms to do even permutati=
ons within orbits.=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
>=20
> MT_ell_sph_dode_E_0-1-0,11 part 2
> > b.PNG>
>=20
> After succeeding with the cornerfaces I'm left with a single corner swap
> !! I have macros to manage the edgefaces, small faces and central faces,
> which do not touch the corners. How can I solve this parity problem ?
> Because a belt of 10 corners is even I can go from 2134567890 to
> 0987654321with 3-cycles (even number of swaps; pay attention to the
> reversed 21 in startposition). Then I have to swap the upper and lower
> ring of 5 corners (5 swaps, odd). Then change direction in each 5-ring
> (even number of swaps). Total : odd number of swaps which is not
> possible with 3-cycles.
> I don't see a solution for the moment.
> Who can help me?
>

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Okay.
Thanks.
I will try.
Kind regards
Ed

----- Original Message -----=20
From: schuma=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, December 03, 2012 5:20 PM
Subject: [MC4D] Re: MagicTile Solving intermediate report


=20=20=20=20
Ed,

You need to first swap the two incorrect 3c corners to fix them. Then you=
need to do two swaps for triangles in two orbits. Although you cannot do o=
ne swap in a single orbit, it turns out you can do two of them simultaneous=
ly: Let A and B be two adjacent edges sharing one vertex. (A,B)*3 does the =
jobs. Please examine which two orbits this algorithm affects and apply it i=
n the correct spot. Then you can use your old algorithms to do even permuta=
tions within orbits.=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
>=20
> MT_ell_sph_dode_E_0-1-0,11 part 2
> _\
> b.PNG>
>=20
> After succeeding with the cornerfaces I'm left with a single corner swa=
p
> !! I have macros to manage the edgefaces, small faces and central faces=
,
> which do not touch the corners. How can I solve this parity problem ?
> Because a belt of 10 corners is even I can go from 2134567890 to
> 0987654321with 3-cycles (even number of swaps; pay attention to the
> reversed 21 in startposition). Then I have to swap the upper and lower
> ring of 5 corners (5 swaps, odd). Then change direction in each 5-ring
> (even number of swaps). Total : odd number of swaps which is not
> possible with 3-cycles.
> I don't see a solution for the moment.
> Who can help me?
>



=20=20
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