Thread: "Cube in a cube (16 moves)"

I originally had it in 28 moves, but I decided to hold off for I was
certain it could be done faster. Even with how it is done now, I'm
betting it can be done in 12 moves. However, here it is. Using these
moves, many variations of the 5^4 cube in a cube can be done, so have
at it!

MagicCube4D 2 0 16 3
000000000000040000000000000
111111111111151111111111111
222222222222262222222222222
333333333333373333333333333
444444444444404444444444444
555555555555515555555555555
666666666666626666666666666
777777777777737777777777777
026:2 510:2 00:2 516:2 414:2 04:2 412:2 022:2 626:2 522:2
60:2 54:2 44:2 64:2 422:2 622:2.

Also, I have a 14 move 2^4 checkerboard using the same moves Remi used
on the 4^4 checkerboard. It's fun to look at, so enjoy.=20
MagicCube4D 2 0 14 2
25525225
43343443
07707007
16616116
61161661
70070770
34434334
52252552
67 317 125 010 010 516 516 44 44 114 114 521 73 221.

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I've called this state: "SUPERDOT". I had 20 twist in my solution. Great jo=
b!

MagicCube4D 2 0 20 3
000000000000070000000000000
111111111111161111111111111
222222222222252222222222222
333333333333343333333333333
444444444444434444444444444
555555555555525555555555555
666666666666616666666666666
777777777777707777777777777
522:2 522:2 34:5 012:2 012:2 34:2 610:-1 316:2 316:2 216:2
612:2 310:2 310:2 616:-1 322:2 014:2 014:2 322:5 54:2 54:2
616:2 014:2.



Ater doing 4^4 in 14 twists I did checkerboard on 2^4 in the same way you d=
id. It looks strange with this type of moves on 2^4, is it?

Sometime ago I've reduced number of twists in 3^4 checerboard (to 24) but I=
cannot do the same with 5^4 (44 twists)

Anyone knows if checkerboard is possible on 2^5 and 4^5? I've tried and tri=
ed but I failed...



---------------------------------------------------------------------------=
----------------------------------------------------

I=20
----- Original Message -----=20
From: spel_werdz_rite=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, June 01, 2008 7:06 PM
Subject: [MC4D] Cube in a cube (16 moves)


I originally had it in 28 moves, but I decided to hold off for I was
certain it could be done faster. Even with how it is done now, I'm
betting it can be done in 12 moves. However, here it is. Using these
moves, many variations of the 5^4 cube in a cube can be done, so have
at it!

MagicCube4D 2 0 16 3
000000000000040000000000000
111111111111151111111111111
222222222222262222222222222
333333333333373333333333333
444444444444404444444444444
555555555555515555555555555
666666666666626666666666666
777777777777737777777777777
026:2 510:2 00:2 516:2 414:2 04:2 412:2 022:2 626:2 522:2
60:2 54:2 44:2 64:2 422:2 622:2.

Also, I have a 14 move 2^4 checkerboard using the same moves Remi used
on the 4^4 checkerboard. It's fun to look at, so enjoy.=20
MagicCube4D 2 0 14 2
25525225
43343443
07707007
16616116
61161661
70070770
34434334
52252552
67 317 125 010 010 516 516 44 44 114 114 521 73 221.

------=_NextPart_000_000D_01C8C44A.645ED660
Content-Type: text/html;
charset="ISO-8859-1"
Content-Transfer-Encoding: quoted-printable

w3c.org/TR/1999/REC-html401-19991224/loose.dtd">

>

That's interesting also because there is a known interesting state on
the 3D cube called "superflip". I mentioned this once before and issued
the following challenge: Produce your shortest solution to this state
that I've called the "superduperflip"

MagicCube4D 2 0 0 3
000010000020304050000060000
111171111121314151111101111
222212222272324202222262222
333313333323730353333363333
444414444424047454444464444
555515555505354575555565555
666606666626364656666676666
777767777727374757777717777
.

Notice that it's quite symmetric and suggest that a short solution may
be possible, but if it really is the proper 4D analog of superflip then
perhaps not.

-Melinda

Remigiusz Durka wrote:
> I've called this state: "SUPERDOT". I had 20 twist in my solution.
> Great job!
>
> MagicCube4D 2 0 20 3
> 000000000000070000000000000
> 111111111111161111111111111
> 222222222222252222222222222
> 333333333333343333333333333
> 444444444444434444444444444
> 555555555555525555555555555
> 666666666666616666666666666
> 777777777777707777777777777
> 522:2 522:2 34:5 012:2 012:2 34:2 610:-1 316:2 316:2 216:2
> 612:2 310:2 310:2 616:-1 322:2 014:2 014:2 322:5 54:2 54:2
> 616:2 014:2.
>
>
>
> Ater doing 4^4 in 14 twists I did checkerboard on 2^4 in the same way
> you did. It looks strange with this type of moves on 2^4, is it?
>
> Sometime ago I've reduced number of twists in 3^4 checerboard (to
> 24) but I cannot do the same with 5^4 (44 twists)
>
> Anyone knows if checkerboard is possible on 2^5 and 4^5? I've tried
> and tried but I failed...

Yeah, I remember both of those posts and was thinking of them as I
made this. I was disappointed to do this and then realize that Remi's
version was of opposite colors. I think even numbered checkers are
impossible in 5D for the same reason they are in 3D. Maybe even
checkers in any odd dimension is impossible. Great discussion for
group theory. =3D)

Melinda, do you think the Superduperflip (I like to call it Hyperflip)
would give us the shortest number of moves to solving the 3^4 as the
Superflip theoretically does for the 3^3?