Hi Nan,
I think it's good idea. I think that any puzzle of this kind deserves a l=
ine in records page. Just change "Size" column to "Size, factor" and add a =
line with "3, 1.15" there.
Strange thing is that, say, for {8,3}, 12 colors you can play with factor=
s 1.15 and 1.4, but not with 1.25. Probably it's a bug in the program.=20
One of nice puzzles is {6,3}, factor=3D1.3 - where circles meet in center=
s. With 4 colors I solved it in 2 twists, but 16 or 25 colors may be funny.
Andrey
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Hi,
>=20
> The puzzle I'm talking is illustrated here:
>=20
> http://wwwmwww.com/Puzzle/MagicTile/3x3x3UDRF.png
>=20
> I came to this puzzle because Carl talked about it in the Twistypuzzles f=
orum
pansion factor" to make deeper cuts. I set it to 1.15 and solved the puzzle=
. The log file has been posted here:
>=20
> This puzzle is essentially Gelatinbrain 3.1.31, except the centers are no=
rmal 3x3x3 centers. Here the edge pieces are quite special. They cannot be =
found in regular 3x3x3. Solving them is quite challenging for me. This is a=
nice, compact and hard puzzle to solve.
>=20
> Note that: for expansion factor =3D 1, {8,3} 6 colors is equivalent to Ru=
bik's cube. However, for expansion factor =3D 1.15, {8,3} 6 colors is not e=
quivalent to Rubik's cube with any expansion factor, because of different g=
eometries.=20
>=20
> I think some puzzles with slicing expansion factor>1 are quite neat (as l=
ong as they turn properly) and can be regarded as standard challenges. What=
are the other nice puzzles with special challenges? We may put some to the=
wiki records page.=20
>=20
> Nan
>
Hi Andrey,
I went through many puzzle with size-3. I believe size-3 is the "first-orde=
r" problems that need to be solved. Here is what I found so far.
Bullet "-" means not interesting because it is (a) too easy to solve or (b)=
directly related to familiar existing puzzles.
Bullet "+" means interesting case because it is (a) not too easy and not to=
o hard and (b) has new features
Bullet "*" means not interesting because it is too complicated and tedious =
to solve (using my patience as a reference).=20
- {n,3} 3 colors: 1 < factor < 1.2. When it turns, it seems to be broken, =
because each edge is moved by two circles into two contradicting directions=
. But the end effect of either direction is the same. Therefore neglecting =
the animation, I still consider it a working puzzle. But anyway, solving is=
trivial. It's solvable in 3~5 moves.
- {6,3} 4 colors: factor =3D 1.2. It can be solved in the same way as fact=
or =3D 1.0. Although it has a new type of pieces, the new pieces will be au=
tomatically solved once the old ones are solved.
- {6,3} 4 colors: factor =3D 1.3. As Andrey said, the pattern is pretty ne=
at, but solving is trivial. It can always be solved within at most 4 moves.=
=20
=20
- {6,3} 4 colors: factor =3D 1.4. Just like {n,3} 3 colors, during turning=
the pieces are "broken". But neglecting the animation, I think of it as a =
working puzzle. Again solving is trivial.
I think the above three cases covers all the {6,3} 4-color puzzles.=20
+ {6,3} 16 and 25 colors: factor =3D 1.3. Neat pattern. The edges are like=
the edges in pyraminx or pyraminx crystal, which can be 3-cycled using a f=
our-move commutator. Therefore solving is nontrivial but not hard.
- {6,3} 16 and 25 colors: factor =3D 1.2. Just a combination of the pieces=
from factor =3D 1.0 and 1.3. Solving is a little bit harder than factor =
=3D 1.0.
* {6,3} 16 and 25 colors: factor =3D 1.4. Too many small pieces. Although =
I can see the algorithms to solve it, I won't enjoy the solving experience =
unless I can use macros.
+ {6,3} 9 colors: factor =3D 1.3. The edge pieces cannot be easily solved =
like in 16 and 25 colors. I don't understand the behavior of them. This see=
ms to be an interesting puzzle.
- {6,3} 9 colors: factor =3D 1.2. It should be similar to the 16/25-color =
case, except the edge pieces should be treated as in factor =3D 1.3.
* {6,3} 9 colors: factor =3D 1.4. Too many small pieces. Seems even harder=
than the 16/25-color case.
+ {7,3} 24 colors (Klein's quartic): factor =3D 1.2. Similar to {6,3} 25 c=
olors. A combination of Klein's quartic with factor =3D 1.0 and pyraminx ed=
ges.
* {7,3} 24 colors (Klein's quartic): factor =3D 1.35 (1.30 is not a sweet =
spot). The situation is similar to {6,3} 25 colors factor =3D 1.4. Too many=
small pieces to solve.
+ {8,3} 6 colors: factor =3D 1.15. It's the puzzle I talked about earlier.=
Regular Rubik's cube plus a special type of edges. A compact and challengi=
ng puzzle.
- {8,3} 6 colors: factor =3D 1.29. This is really a weird looking puzzle. =
Neglecting glitchy animation, I find it an interesting one. When it's scram=
bled, it looks weird, weird, weird. At the center of each circle there is a=
daisy with eight petals. In principle it is equivalent to Rubik's cube but=
you always turn two faces (e.g. R and MR, it is equivalent to turning L' a=
nd reorient the cube). The checkerboard pattern on the Rubik's cube looks m=
ore like a "daisy" pattern in this puzzle. A snapshot of such pattern can b=
e found here: http://f1.grp.yahoofs.com/v1/gHl8TQM7KVekRGSLFshClhWBghiXnOq6=
JjY0g8rfXHDlDthzbbJpTTY1pDV0ByHELCAP8ji9dppnRq_hs2-aduIUCLoPGpnP/Nan%20Ma/8=
3_6colors_size3_129.PNG
+ {8,3} 12 colors: factor =3D 1.15. The edges behave like {6,3} 9 colors f=
actor =3D 1.2. I don't understand but seems interesting.
* {8,3} 12 colors: factor =3D 1.29. Similar to {6,3} 9 colors factor =3D 1=
.4. Too many small pieces.=20
Puzzles {n,3} for n>9 are similar to the smaller counterparts with the same=
number of colors.=20
- Dodecahedron 12 colors. As Brandon pointed out earlier, the face-turning=
dodecahedron with cuts of different depths has been well studied:
al values for the factor and the puzzles are always covered by Gelatinbrain=
1.1.1 ~ 1.1.5. Therefore although this is a very rich family of nice puzzl=
es, it's not unique in Magic Tile.=20
+ Hemi-Dodecahedron 6 colors. Another rich family of puzzles, whereas this=
family is unique in Magic Tile. I interpret them as slice-only face-turnin=
g dodecahedra. For example, if factor =3D 1.75, it's a slice-only Starminx.=
Unfortunately I cannot find the sweet spot to make a slice-only pyraminx c=
rystal. The tiny pieces are always around.=20
For size-5 puzzles, I tried to analyze {8,3} 6 colors factor 1.15. It seems=
to be a pretty hard puzzle. I don't think I'm patient enough to solve it w=
ithout using macros. Generally speaking I think size-5 is too complicated.=
=20
Nan
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Hi Nan,
> I think it's good idea. I think that any puzzle of this kind deserves a=
line in records page. Just change "Size" column to "Size, factor" and add =
a line with "3, 1.15" there.
> Strange thing is that, say, for {8,3}, 12 colors you can play with fact=
ors 1.15 and 1.4, but not with 1.25. Probably it's a bug in the program.=20
> One of nice puzzles is {6,3}, factor=3D1.3 - where circles meet in cent=
ers. With 4 colors I solved it in 2 twists, but 16 or 25 colors may be funn=
y.
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Hi,
> >=20
> > The puzzle I'm talking is illustrated here:
> >=20
> > http://wwwmwww.com/Puzzle/MagicTile/3x3x3UDRF.png
> >=20
> > I came to this puzzle because Carl talked about it in the Twistypuzzles=
forum
expansion factor" to make deeper cuts. I set it to 1.15 and solved the puzz=
le. The log file has been posted here:
> >=20
> > This puzzle is essentially Gelatinbrain 3.1.31, except the centers are =
normal 3x3x3 centers. Here the edge pieces are quite special. They cannot b=
e found in regular 3x3x3. Solving them is quite challenging for me. This is=
a nice, compact and hard puzzle to solve.
> >=20
> > Note that: for expansion factor =3D 1, {8,3} 6 colors is equivalent to =
Rubik's cube. However, for expansion factor =3D 1.15, {8,3} 6 colors is not=
equivalent to Rubik's cube with any expansion factor, because of different=
geometries.=20
> >=20
> > I think some puzzles with slicing expansion factor>1 are quite neat (as=
long as they turn properly) and can be regarded as standard challenges. Wh=
at are the other nice puzzles with special challenges? We may put some to t=
he wiki records page.=20
> >=20
> > Nan
> >
>