Hi everyone,
In the last three days I solved 3^4 alt, 2x2x3x3 and 2x3x4x5 on MPUlt. Actu=
ally before that I tried the 120-cell on MPUlt. After spending 3 hours on i=
t, I decided I was not patient enough to do it. So I switched to small puzz=
les. The common property that three puzzles share is that they are all "sub=
groups" of tesseract puzzles. However, I have quite different experience so=
lving them.=20
------------
1. 3^4 alt (turning around 2C by 180 deg and 4C by 120 deg)
When I first thought of this puzzle, I was imagining the 180-deg-only Rubik=
's Cube. Please try to scramble and solve a Rubik's Cube using only 180 deg=
turns. It's pretty simple and very different from the common Rubik's Cube.=
3^4 alt, however, is not that different from 3^4.=20
2C pieces behave in the same way as in 3^4, except odd permutations are for=
bidden. Flipping two 2C's is possible.
Two 3C pieces can be rotated simultaneously (the permutation of stickers of=
each piece is a 3-cycle), but not flipped ((a,b,c)->(b,a,c) is impossible)=
in place. Note that in 3^4 the latter thing is possible.
4C vertices belong to two orbits. Before solving it I only prepared the alg=
orithms for rotating two 4C pieces in the same orbit (the permutation of th=
e stickers on each 4C is a 3-cycle). But I met the situation that I needed =
to rotate two 4C in different orbits. It was a surprise and I had to re-sol=
ve a large fraction of the puzzle.
Overall, 3^4 alt is quite similar to 3^4.=20
-------------
2. 2x2x3x3 (turning around square by 90 deg and rectangles by 180 deg)
This puzzle is similar to the duoprisms in MC4D. The cells are of two kinds=
: 2x3x3 cells and 2x2x3 cells. Stickers in one type of cells never visit th=
e other type of cells. The above properties are shared with all the duopris=
ms.=20
Compared with the duoprims in MC4D, 2x2x3x3 is a really small puzzle. Once =
the algorithms are ready, it doesn't take long at all to solve it.
----------
3. 2x3x4x5 (180-deg only)
This puzzle is truly similar to the 180-deg only 3D puzzles: each sticker c=
an only stay in the original cell or the antipodal cell.=20
The direct analog in 3D should be 2x3x4 and 3x4x5. I have solved 2x3x4 and =
3x4x5 on a simulator. So I pulled out my notes for them. What I found was p=
retty vague, like, "use algorithms like [R,u]x3 cleverly". I don't have a s=
ystematic analysis for this kind of puzzle. Usually I just try my best to s=
olve one or two pieces, and sometimes magically the others fall into the co=
rrect slots. It seems like many pieces are strongly correlated. But I don't=
understand the relation between pieces. Sometimes I solve centers first an=
d sometimes corners first.=20
So I had to boldly go to 2x3x4x5 and hoped magic happened again. I was not =
that lucky.=20
It took me a long long time to solve it. The method was again very heuristi=
c. At the end I was solving 3C pieces. Once I saw a situation, I had to loo=
k for algorithms ad hoc. Application of macros is limited in this puzzle, b=
ecause a macro recorded on a, say, 2x3x4 cell cannot be used on a 2x3x5 cel=
l. So I alternated between a testing log file and a solving log file severa=
l times.=20
To give you an idea how frustrated I was, let me tell you this: just now I =
tried to revisit 2x3x4x5. But after two minutes I was lost again. I didn't =
know what to do, because I've never found a systematic solution.
--------
This is my story of solving the three "subgroups" of the cube. 3^4 alt is v=
ery similar to 3^4; 2x2x3x3 is basically a duoprism; 2x3x4x5 is solved heur=
istically, with pain.=20
Nan
Hi Nan,
Your notes are very interesting! Thanks a lot!
Ed
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Hi everyone,
>=20
> In the last three days I solved 3^4 alt, 2x2x3x3 and 2x3x4x5 on MPUlt. Ac=
tually before that I tried the 120-cell on MPUlt. After spending 3 hours on=
it, I decided I was not patient enough to do it. So I switched to small pu=
zzles. The common property that three puzzles share is that they are all "s=
ubgroups" of tesseract puzzles. However, I have quite different experience =
solving them.=20
>=20
> ------------
> 1. 3^4 alt (turning around 2C by 180 deg and 4C by 120 deg)
>=20
> When I first thought of this puzzle, I was imagining the 180-deg-only Rub=
ik's Cube. Please try to scramble and solve a Rubik's Cube using only 180 d=
eg turns. It's pretty simple and very different from the common Rubik's Cub=
e. 3^4 alt, however, is not that different from 3^4.=20
>=20
> 2C pieces behave in the same way as in 3^4, except odd permutations are f=
orbidden. Flipping two 2C's is possible.
>=20
> Two 3C pieces can be rotated simultaneously (the permutation of stickers =
of each piece is a 3-cycle), but not flipped ((a,b,c)->(b,a,c) is impossibl=
e) in place. Note that in 3^4 the latter thing is possible.
>=20
> 4C vertices belong to two orbits. Before solving it I only prepared the a=
lgorithms for rotating two 4C pieces in the same orbit (the permutation of =
the stickers on each 4C is a 3-cycle). But I met the situation that I neede=
d to rotate two 4C in different orbits. It was a surprise and I had to re-s=
olve a large fraction of the puzzle.
>=20
> Overall, 3^4 alt is quite similar to 3^4.=20
>=20
> -------------
> 2. 2x2x3x3 (turning around square by 90 deg and rectangles by 180 deg)
>=20
> This puzzle is similar to the duoprisms in MC4D. The cells are of two kin=
ds: 2x3x3 cells and 2x2x3 cells. Stickers in one type of cells never visit =
the other type of cells. The above properties are shared with all the duopr=
isms.=20
>=20
> Compared with the duoprims in MC4D, 2x2x3x3 is a really small puzzle. Onc=
e the algorithms are ready, it doesn't take long at all to solve it.
>=20
> ----------
> 3. 2x3x4x5 (180-deg only)
>=20
> This puzzle is truly similar to the 180-deg only 3D puzzles: each sticker=
can only stay in the original cell or the antipodal cell.=20
>=20
> The direct analog in 3D should be 2x3x4 and 3x4x5. I have solved 2x3x4 an=
d 3x4x5 on a simulator. So I pulled out my notes for them. What I found was=
pretty vague, like, "use algorithms like [R,u]x3 cleverly". I don't have a=
systematic analysis for this kind of puzzle. Usually I just try my best to=
solve one or two pieces, and sometimes magically the others fall into the =
correct slots. It seems like many pieces are strongly correlated. But I don=
't understand the relation between pieces. Sometimes I solve centers first =
and sometimes corners first.=20
>=20
> So I had to boldly go to 2x3x4x5 and hoped magic happened again. I was no=
t that lucky.=20
>=20
> It took me a long long time to solve it. The method was again very heuris=
tic. At the end I was solving 3C pieces. Once I saw a situation, I had to l=
ook for algorithms ad hoc. Application of macros is limited in this puzzle,=
because a macro recorded on a, say, 2x3x4 cell cannot be used on a 2x3x5 c=
ell. So I alternated between a testing log file and a solving log file seve=
ral times.=20
>=20
> To give you an idea how frustrated I was, let me tell you this: just now =
I tried to revisit 2x3x4x5. But after two minutes I was lost again. I didn'=
t know what to do, because I've never found a systematic solution.
> --------
>=20
> This is my story of solving the three "subgroups" of the cube. 3^4 alt is=
very similar to 3^4; 2x2x3x3 is basically a duoprism; 2x3x4x5 is solved he=
uristically, with pain.=20
>=20
> Nan
>