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标题: 一阶魔方， 1×1×1 [打印本页]

作者: bardy 时间: 2009-5-16 10:57:00 标题: 一阶魔方， 1×1×1

一般是三阶魔方，即 3×3×3，

复杂一点的有四阶的 4×4×4

简单一点的有二阶的 2×2×2

有没人想过最简单的一阶 1×1×1 呢？（有 0×0×0吗？）

研究过吗

如果考虑魔方整体方向的话，一阶魔方共有 24 种状态。所以用穷举法分析也是很简单的

在网上搜索了一下，十几年前还是有老外对这个简单的一阶魔方也做过详细的研究，
也不知道是为了什么？

简单地说，魔方越来越简化，
在三阶魔方中的 RL' 这种旋转方式放在二阶魔方中的话，就退化成了一次魔方整体旋转
二阶魔方中的 R 或 L 之类的旋转在一阶魔方中都退化成了魔方的整体旋转

不考虑魔方的整体方向的话，一阶魔方就只有一种状态了，无所谓还原什么的了
但事实上三阶魔方一般也都是要考虑魔方的方向的，国际比赛的标准是什么？
估计一般都是上白前绿吧。

如果考虑魔方整体方向的话，一阶魔方共有 24 种状态。所以用穷举法分析也是很简单的

要把一个想起来很简单的东西说得清楚透彻也不是件简单的事啊，愿意的话请看原文：

Date: Tue, 14 Nov 95 09:13:41 -0400 1995年十一月

God's Algorithm for the 1x1x1 Rubik's Cube

Solving the 1x1x1 Rubik's cube is probably a bit silly and whimsical, but
let's look at it anyway.

I was led in this direction by rereading some articles in the archives
from Dan Hoey and others concerning NxNxN Rubik's cubes.  For example,
consider Dan's discussion "Cutism, Slabism, and Eccentric Slabism" from
1 June 83 19:39:00.  Sometimes degenerate cases are slightly interesting.
I guess the 1x1x1 case is the most degenerate we have, unless you want to
consider the 0x0x0.

It seems to me that either cutism or slabism, as Dan calls them, reduce to
whole cube rotations for the 1x1x1 case.  For example, a quarter turn face
turn or a quarter turn slice would be interpreted as a whole cube quarter
turn for the 1x1x1.  Hence, the cube group for the 1x1x1 is simply C, the
group of 24 rotations of the cube.

By analogy with some of our previous work, I can think of essentially
three different ways to model the 1x1x1.

1)  With the 2x2x2, we normally wish to consider the puzzle solved if
each face is all of one color.  That is, whole cube rotations are
to be considered equivalent.  With the Singmaster fixed face
center view of the 3x3x3, the issue of whole cube rotations does
not arise.  But with the 2x2x2 we would normally consider
(for example) RL' equivalent to I.  The most common way to
accomplish this type of equivalence is to fix one of the corners.

If we fix one of the corners of the 1x1x1, then we have a most
remarkable puzzle.  There is only one state, nothing can ever
move, and the puzzle is always solved.

2)  A second way to model the 2x2x2 such that whole cube rotations are
considered to be equivalent is to consider the set of states to be
the set of cosets of C, that is, the set of all xC.

If we take this approach with the 1x1x1, then there is only one
coset, namely iC (or just C, if you prefer).  The cube can rotate,
but all 24 states are considered to be equivalent and the puzzle
is always solved.

3)  Finally, if you model the 2x2x2 in such a way that whole cube
rotations are considered to be distinct, then you are really
modelling the corners of the 3x3x3.  Indeed, a naive program
that simply modelled the permutations of the 2x2x2 facelets would
in fact unwittingly be modelling the corners of the 3x3x3.

If you take the same approach of modelling the permutations of the
1x1x1 facelets, then you in effect are considering whole
cube rotations to be distinct.  You have a very easy problem,
but the problem is not totally trivial as it is with approach #1
or approach #2.  The rest of this note will therefore consider the
problem of the 1x1x1 cube where whole cube rotations are considered
to be distinct.

Since we need to deal with whole cube rotations, I will use lower case
letters as our standard E-mail simulation of Frey and Singmaster's script
notation for whole cube quarter turns -- t for Top, r for Right, etc.  We
need only three of the six letters because, for example, we have l=r',
d=t', b=f', etc.  I will use t, r, and f.

We know before we start that there are 24 states.  We also know before we
start that these 24 states form 5 M-conjugacy classes, where M is the set
of 48 rotations and reflections of the cube.  (There are 10 M-conjugacy
classes of M, of which 5 are rotations and 5 are reflections.) Hence, any
discussion of God's algorithm will involve 5 conjugacy classes and 24
states.

The obvious searches to look at are for qturns only, and for qturns plus
hturns.  We may generate the qturn case as C=<t,r,f>.  We may generate
the qturn plus hturn case as C=<t,r,f,t2,r2,f2>.

Qturns Only
Distance Conjugacy Positions
from    Classes
Start
0       1       1  {i}
1       1       6  {t,t',r,r',f,f'}
2       2    11  {tt,rr,ff},{tr,tr',tf,tf',t'r,t'r',t'f,t'f'}
3       1       6  {ttf,ttf',ffr,ffr',rrt,rrt'}
---       ----    ----
Total       5    24
Qturns Plus Hturns
Distance Conjugacy Positions
from    Classes
Start
0       1       1  {i}
1       2       9  {t,t',r,r',f,f'},{t2,r2,f2}
2       2    14  {tr,tr',tf,tf',t'r,t'r',t'f,t'f'},
                     {t2f,t2f',f2r,f2r',r2t,r2t'}
---    ----    ----
Total    5    24

There are some additional problems we can look at.  For an example, an
interesting problem on the 3x3x3 is variously called the stuck axle
problem or the five generator problem.  In the case of the 1x1x1, we have
the "two generator problem" because we certainly can generate C as C=<t,f>
(Proof: r=tft').  But can we generate C with only one generator?  The
answer is no.  (Proof:  Order(i)=1, Order(t)=4, Order(tt)=2, Order(tf)=3,
and Order(ttf)=2.  All the orders are less than 24.  Note that it suffices
to calculate the order for one representative of each conjugacy class.)  I
will leave it as an exercise for the reader to determine the lengths of
each of the 24 positions if we generate C as <t,f>, and to determine the
appropriate conjugacy classes to take into account the symmetry of C
generated as <t,f>.

By the way, do we know the minimum number of generators required to
generate the 3x3x3?  Here I do not mean the minimum number of quarter
turns.  I am asking the question if we are permitted to use as generators
any elements of G.

Here is one final item about the 1x1x1.  We do not know how many subgroups
of G there are for the 3x3x3.  But we do know how many subgroups of C
there are.  There has been much discussion of the 98 subgroups of M which
can be arranged in 33 conjugacy classes.  The subgroups of C are simply
those subgroups of M which consist entirely of rotations.  There are 30
such subgroups, and they may be arranged in 11 conjugacy classes.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)             jbryan@pstcc.cc.tn.us

[ 本帖最后由 bardy 于 2009-5-16 14:35 编辑 ]

作者: wjfstam 时间: 2009-5-16 11:00:48

人手一个0×0×0

1×1×1感觉只能当手机链

作者: Vicki 时间: 2009-5-16 11:06:32

1x1x1我做过一个~

在图中中间上面的位置~

-----------------------------

注意：我不是楼主~

[ 本帖最后由 Vicki 于 2009-5-18 18:26 编辑 ]

附件: 魔方20090425.jpg (2009-5-16 11:06:32, 380.65 KB) / 下载次数 217
http://bbs.mf8-china.com/forum.php?mod=attachment&aid=NTA2MjB8ZDVjZGYyZmZ8MTczMjUyNTIwOHwwfDA%3D

作者: Vicki 时间: 2009-5-16 11:08:58

其实一阶严格来说不能算是魔方~

乌木还是大烟头说过：有相交的旋转面才能称作魔方~

所以最简单的魔方是1x2x2~

http://bbs.mf8-china.com/viewthread.php?tid=28193

作者: 515761153 时间: 2009-5-16 11:11:46

1x1x2呢?
好像都能玩

作者: 515761153 时间: 2009-5-16 11:13:07

对不起
说错话了...

作者: 梦楠 时间: 2009-5-16 11:13:53

这张照片是俯视阿·！呵呵

作者: bardy 时间: 2009-5-16 11:17:52

有没有仔细研究过的？我在搜索

作者: 老魔新手 时间: 2009-5-16 11:24:06

随便找一个角块，去掉棱脚，补成方块，就是1X1X1。

作者: everest 时间: 2009-5-16 11:26:02

没见过一阶的.............

作者: bardy 时间: 2009-5-16 11:46:17 标题: God's Algorithm for the 1x1x1 Rubik's Cube

在网上搜索了一下，有老外还是对这个简单的一阶魔方也做过详细的研究，
也不知道是为了什么？

简单地说，魔方越来越简化，
在三阶魔方中的 RL' 这种旋转方式放在二阶魔方中的话，就退化成了一次魔方整体旋转
二阶魔方中的 R 或 L 之类的旋转在一阶魔方中都退化成了魔方的整体旋转

不考虑魔方的整体方向的话，一阶魔方就只有一种状态了，无所谓还原什么的了
但事实上三阶魔方一般也都是要考虑魔方的方向的，国际比赛的标准是什么？
估计一般都是上白前绿吧。

如果考虑魔方整体方向的话，一阶魔方共有 24 种状态。所以用穷举法分析也是很简单的

Date: Tue, 14 Nov 95 09:13:41 -0400 1995年十一月

God's Algorithm for the 1x1x1 Rubik's Cube
Solving the 1x1x1 Rubik's cube is probably a bit silly and whimsical, but
let's look at it anyway.
I was led in this direction by rereading some articles in the archives
from Dan Hoey and others concerning NxNxN Rubik's cubes.  For example,
consider Dan's discussion "Cutism, Slabism, and Eccentric Slabism" from
1 June 83 19:39:00.  Sometimes degenerate cases are slightly interesting.
I guess the 1x1x1 case is the most degenerate we have, unless you want to
consider the 0x0x0.
It seems to me that either cutism or slabism, as Dan calls them, reduce to
whole cube rotations for the 1x1x1 case.  For example, a quarter turn face
turn or a quarter turn slice would be interpreted as a whole cube quarter
turn for the 1x1x1.  Hence, the cube group for the 1x1x1 is simply C, the
group of 24 rotations of the cube.
By analogy with some of our previous work, I can think of essentially
three different ways to model the 1x1x1.

1)  With the 2x2x2, we normally wish to consider the puzzle solved if
each face is all of one color.  That is, whole cube rotations are
to be considered equivalent.  With the Singmaster fixed face
center view of the 3x3x3, the issue of whole cube rotations does
not arise.  But with the 2x2x2 we would normally consider
(for example) RL' equivalent to I.  The most common way to
accomplish this type of equivalence is to fix one of the corners.
If we fix one of the corners of the 1x1x1, then we have a most
remarkable puzzle.  There is only one state, nothing can ever
move, and the puzzle is always solved.
2)  A second way to model the 2x2x2 such that whole cube rotations are
considered to be equivalent is to consider the set of states to be
the set of cosets of C, that is, the set of all xC.
If we take this approach with the 1x1x1, then there is only one
coset, namely iC (or just C, if you prefer).  The cube can rotate,
but all 24 states are considered to be equivalent and the puzzle
is always solved.
3)  Finally, if you model the 2x2x2 in such a way that whole cube
rotations are considered to be distinct, then you are really
modelling the corners of the 3x3x3.  Indeed, a naive program
that simply modelled the permutations of the 2x2x2 facelets would
in fact unwittingly be modelling the corners of the 3x3x3.
If you take the same approach of modelling the permutations of the
1x1x1 facelets, then you in effect are considering whole
cube rotations to be distinct.  You have a very easy problem,
but the problem is not totally trivial as it is with approach #1
or approach #2.  The rest of this note will therefore consider the
problem of the 1x1x1 cube where whole cube rotations are considered
to be distinct.

Since we need to deal with whole cube rotations, I will use lower case
letters as our standard E-mail simulation of Frey and Singmaster's script
notation for whole cube quarter turns -- t for Top, r for Right, etc.  We
need only three of the six letters because, for example, we have l=r',
d=t', b=f', etc.  I will use t, r, and f.
We know before we start that there are 24 states.  We also know before we
start that these 24 states form 5 M-conjugacy classes, where M is the set
of 48 rotations and reflections of the cube.  (There are 10 M-conjugacy
classes of M, of which 5 are rotations and 5 are reflections.) Hence, any
discussion of God's algorithm will involve 5 conjugacy classes and 24
states.
The obvious searches to look at are for qturns only, and for qturns plus
hturns.  We may generate the qturn case as C=<t,r,f>.  We may generate
the qturn plus hturn case as C=<t,r,f,t2,r2,f2>.

Qturns Only
Distance Conjugacy Positions
from    Classes
Start
0       1       1  {i}
1       1       6  {t,t',r,r',f,f'}
2       2    11  {tt,rr,ff},{tr,tr',tf,tf',t'r,t'r',t'f,t'f'}
3       1       6  {ttf,ttf',ffr,ffr',rrt,rrt'}
---       ----    ----
Total       5    24
Qturns Plus Hturns
Distance Conjugacy Positions
from    Classes
Start
0       1       1  {i}
1       2       9  {t,t',r,r',f,f'},{t2,r2,f2}
2       2    14  {tr,tr',tf,tf',t'r,t'r',t'f,t'f'},
                     {t2f,t2f',f2r,f2r',r2t,r2t'}
---    ----    ----
Total    5    24

There are some additional problems we can look at.  For an example, an
interesting problem on the 3x3x3 is variously called the stuck axle
problem or the five generator problem.  In the case of the 1x1x1, we have
the "two generator problem" because we certainly can generate C as C=<t,f>
(Proof: r=tft').  But can we generate C with only one generator?  The
answer is no.  (Proof:  Order(i)=1, Order(t)=4, Order(tt)=2, Order(tf)=3,
and Order(ttf)=2.  All the orders are less than 24.  Note that it suffices
to calculate the order for one representative of each conjugacy class.)  I
will leave it as an exercise for the reader to determine the lengths of
each of the 24 positions if we generate C as <t,f>, and to determine the
appropriate conjugacy classes to take into account the symmetry of C
generated as <t,f>.
By the way, do we know the minimum number of generators required to
generate the 3x3x3?  Here I do not mean the minimum number of quarter
turns.  I am asking the question if we are permitted to use as generators
any elements of G.
Here is one final item about the 1x1x1.  We do not know how many subgroups
of G there are for the 3x3x3.  But we do know how many subgroups of C
there are.  There has been much discussion of the 98 subgroups of M which
can be arranged in 33 conjugacy classes.  The subgroups of C are simply
those subgroups of M which consist entirely of rotations.  There are 30
such subgroups, and they may be arranged in 11 conjugacy classes.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)             jbryan@pstcc.cc.tn.us

作者: bardy 时间: 2009-5-16 12:05:17 标题: 伪正经

也有伪正经的

比如下面这个分析得也很详细，不过没有幽默细胞的恐怕理解不了

AH, the 1x1x1.

Did you know....................

The 1x1x1 Rubik's Cube is by far "The Most Difficult Puzzle Of All Time™". Many have scrambled, twisted and turned this mythical puzzle, but few have solved it. By the end of this article, YOU TOO will be able to solve this puzzle.
Contents
[hide]

* 1 Only One Combination, Only One Solution!
* 2 Meet Your Cube
o 2.1 Center cubes (1)
o 2.2 Edge cubes (1)
o 2.3 Corner cubes (1)
* 3 Twisting Hints
* 4 Notation
* 5 How To Make Your 1x1x1 Rubik's Cube Rotate Faster
o 5.1 Don't Lubricate your 1x1x1 Rubik's Cube Right Away
o 5.2 How to Disassemble your 1x1x1 Rubik's Cube
o 5.3 Recommended Lubricants
* 6 How To Solve The 1x1x1 Rubik's Cube
* 7 How to Cheat When Solving the 1x1x1 Rubik's Cube
* 8 Cube Games And Patterns
o 8.1 Patterns For The Experienced Solver
o 8.2 Games For All Ages
* 9 Research On The 1x1x1 Rubik's Cube
* 10 Links

Your 1x1x1 Rubik's Cube is the incredibly addictive, multi-dimensional challenge that has fascinated puzzle fans around the world.

Any permutation of the 1 corner cubie is possible (1! positions), and 1 cubie can be independently rotated (11 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 1.

The 1x1x1 Rubik's Cube has been called "the perfect puzzle" and "the best puzzle ever". You can solve the 1x1x1 Rubik's Cube from any starting point. With the right twists, anybody can do it. And with only ONE combination, every challenge is always the same!
[edit] Meet Your Cube
The 1x1x1 Rubik's Cube, Eaten with only centre cubes.
The 1x1x1 Rubik's Cube, Eaten with only centre cubes.

The 1x1x1 Rubik's Cube has 6 sides, or faces. Each face is a different solid color when the 1x1x1 Rubik's Cube is solved.

Your cube is made up of one (1) cube piece, which is simultaneously a centre cube, an edge cube, and a corner cube, making the 1x1x1 Rubik's Cube more difficult than any other. This cube piece can be rotated, but is otherwise stationary.
[edit] Center cubes (1)

Center cubes have 6 colors, six times as many as the standard Rubik's Cube. Although the colors can rotate in place, they do not move independently from one face of the cube to another. In other words, blue is always opposite white, red is always opposite orange, and green is always opposite yellow. Center cubes determine the color of the face they're in.

A standard Rubik's Cube can be solved with any of the center cubes in any of four rotations. A 1x1x1 cube can only be solved with each of the center cubes in one specific rotation with respect to the others. This alone makes it over a thousand times(4x4x4x4x4x4)as difficult to solve as the standard Rubik's cube.

Each edge cube has 6 colours on it, 3 colours of which are ordinarily hidden from direct view. These are not in fixed positions like centre cubes.

There are 6 colours on each corner cube, and all one of the corner cubes rotate in tandem every time the configuration is changed.

Each face can't be turned independently. Try it. (Doing this won't mix up the cube pieces, but will change the colours which face you at a given time.)
[edit] Twisting Hints
Did you know...
that if you saw every combination of the 1x1x1 Rubik's Cube, at a rate of one per second, it would take you less than ONE SECOND to see all the combinations?
An expert solving the 1x1x1 Rubik's Cube WAY faster than you can. just give up.
An expert solving the 1x1x1 Rubik's Cube WAY faster than you can. just give up.

The easiest way to solve the 1x1x1 Rubik's Cube is layer by layer, starting at the top. It is very difficult to solve face by face, and with only one combination, nearly always possible to solve by trial and error.

Always hold the 1x1x1 Rubik's Cube in the same orientation while completing a layer. Remember the colours of the top centre cube and the centre cube facing you.

On a 1x1x1 Rubik's Cube, opposite colours always appear on the same cube piece. The 1x1x1 cube is the only Rubik's Cube on which opposite colors can appear on the same cubie. For example, any cube piece will have both blue and white, which are opposites, in its colour scheme. It helps to remember which colours are opposites when solving your 1x1x1 Rubik's Cube, while when using a larger cube, you can never know what color cubies are on the opposite side.

Sometimes you'll perform a series of twists to get a single cube into position. Doing that will often get other cubes out of position. Repeat the series of twists backwards to restore the cube.
[edit] Notation

When writing down algorithms used for the 1x1x1 Rubik's Cube, experts use certain letters to signify which sides are being rotated. here is a list of notations:

W means rotate the white face 90 degrees clockwise

Y means rotate the yellow face 90 degrees clockwise

B means rotate the blue face 90 degrees clockwise

O means rotate the orange face 90 degrees clockwise

G means rotate the green face 90 degrees clockwise

R means rotate the red face 90 degrees clockwise

G means rotate the green face 90 degrees clockwise. It's listed twice because G is a badass letter.

Sometimes, after a letter is written, you will see the number two (2). This means that you rotate that face 180 degrees.
[edit] How To Make Your 1x1x1 Rubik's Cube Rotate Faster

You may notice that at first, your Rubik's Cube may not rotate as fast as you had hoped it would. This problem can be solved by applying lubricant to the inside of your cube. Here are some tips on how to "lube your cube":
[edit] Don't Lubricate your 1x1x1 Rubik's Cube Right Away

When you first open your brand new 1x1x1 Rubik's Cube, you will probably want to lubricate it right away. However, this is not recommended. For if you lube it immediately, it might seem fine at first, but after about a day, you will realize that the lubricant has worn off.

However, if you really just can't wait to lube your cube, it is recommended that you use sandpaper to wear down the inside before you apply the lubricant.
[edit] How to Disassemble your 1x1x1 Rubik's Cube

The 1x1x1 Rubik's Cube is much more difficult to disassemble than larger cubes. this is because it is made up of only one cubie. Therefore, you will have to apply a lot of strength to break open the 1x1x1 cube. Few have been able to disassemble the cube without permanently breaking it.
[edit] Recommended Lubricants

Here is a list of lubricants recommended by 1x1x1 speedcubers:

1. Silicone Oil

2. Petroleum Jelly (Vaseline)

3. WD-40

4. Other Oils/Greases That You Can Find Around Your House Or Garage

When solved, every face of the 1x1x1 Rubik's Cube is a solid colour. Once you start turning, twisting and flipping, it's easy to mix up the colours. Not to worry - the 1x1x1 Rubik's Cube can be set right from any mixed-up combination.

1. Choose a colour. This will be your top face. Turn your 1x1x1 Rubik's Cube so that the centre cube on the top face is that colour.
2. Solve the top face, by using quarter- and half-twists. Don't worry if you find this step challenging, this is often the longest and hardest step in solving your 1x1x1 Rubik's Cube.
3. Rotate the 1x1x1 rubik's cube along an axis that is not along the plane of the square that is now on top, and perpendicular to one of the other faces so as to rotate an uncompleted face to the top.
4. Repeat steps 1-3 with all other colors.
5. Brag to all your friends on how YOU SOLVED THE 1x1x1 RUBIK'S CUBE!

Method 1:

1. Before scrambling, note the correct position of the colours on the cube.
2. Scramble cube.
3. Choose a colour. This will be your top face. Turn your 1x1x1 Rubik's Cube so that the centre cube on the top face is that colour.
4. Remove all the stickers except for the one on the top face, so you have only one sticker remaining on your cube. Preferably remove with fingernails or exacto knife.
5. Re-attach stickers in the correct positions, as you noted in Step 1. If you didn't do that, too bad.

Method 2:

1. Disassemble your 1x1x1 Rubik's Cube
2. Put the disassembled cube pieces in such a manner to form the original cube.

Method 3:

1. Detach all stickers of your 1x1x1 Rubik's Cube.
2. Colour in the now empty faces with your choice of paint.

(Note that oil paints may take an extended period of time to dry, so if using oil based paints, apply thinly.)

Method 4:

1. Run to the store
2. Buy a brand new 1x1x1 Rubik's Cube.
3. There you have it! A solved 1x1x1 Rubik's Cube!!!

Method 5: Ask a professional to solve it for you.
[edit] Cube Games And Patterns
Did you know...
that theoretically the longest path to solving the 1x1x1 Rubik's Cube is in as many as FIVE twists. So far no one has succeeded in demonstrating this method.

作者: bardy 时间: 2009-5-16 12:07:07

After solving the 1x1x1 Rubik's Cube, you may wonder, "What else is there to do?". This section is only for those experts that have solved the 1x1x1 Rubik's Cube many times, and can do so from any combination.
[edit] Patterns For The Experienced Solver

There are almost an infinite number of beautiful patterns you can make with your 1x1x1 Rubik's Cube. Here is the complete list:

1

Don't be just limited to the vast range of patterns! Entertain yourself and others with these family friendly fun games.

* Place it in a bowl of jelly cubes, and see who gets injured!
* Paint your cube's blue side black and hand it to a colleague. Threaten to shoot him if he can't turn the blue face up!!
* Grind into a fine powder, and mix into your next cake. Give a prize to the person who figures it out first, or the first one to be hospitalised.
* Have a competition and see who can solve the 1x1x1 Rubik's Cube in the longest amount of time.
* Flip the cube upside down. Your inexperienced guests won't know where that top face disappeared to! Take advantage of your less able friends.
* Amaze your friends with your intimate knowledge of the 0x0x0 InfraCube. Explain that you received your unique insight from Rubiko, the god of all cubes.
* Have a competition to see who makes a regular pattern different to that of the completed 1x1x1 Rubik's Cube first
* Have a competition to see who can solve a 1x1x1 Rubik's Cube blindfolded
* Have a competition to see who can solve the 1x1x1 Rubik's Cube in their mouth
* Have a competition to see who can't solve the 1x1x1 Rubik's Cube

Research On The 1x1x1 Rubik's Cube

Researchers at Ivy League colleges have done vast research on the 1x1x1 Rubik's Cube. They found that no matter how scrambled the cube is, it can be solved in as little as zero (0) steps, every time. In addition, they have built a robot that can solve a 1x1x1 Rubik's Cube.

大学研究员对1x1x1 的一阶魔方作了大量的研究。他们经研究发现任意打乱的一维魔方都是可以还原的。
并且还可以造出一个能够还原一阶魔方的机器人。

[ 本帖最后由 bardy 于 2009-5-16 12:10 编辑 ]

作者: Ricky.C 时间: 2009-5-16 12:08:45

1X1X1 一早就有了

0X0X0 你玩空氣嗎?

作者: juventus66 时间: 2009-5-16 12:12:29

1X1X1就一个方块而已

作者: bardy 时间: 2009-5-16 12:13:11

原帖由 CTS 于 2009-5-16 12:08 发表
1X1X1 一早就有了

呵呵，我是想找一下详细的研究。以科学的态度

我看很多人可以学习一下，怎样把一件事情说得清楚明白

科学要怎么做，学问要怎么做。该详细的时候还是需要详细的

作者: bardy 时间: 2009-5-16 12:14:06

原帖由 juventus66 于 2009-5-16 12:12 发表
1X1X1就一个方块而已

看似简单的东西也不一定能够简单的说清楚，仔细想想也是可以研究一下的

作者: bardy 时间: 2009-5-16 12:19:12

Records

* Chuck Norris (-0.01 seconds), also holds the record for the -1x-1x-1 Rubik's Cube

哈哈，在网上居然搜索到了这个： -1 x -1 x -1

作者: 才源 时间: 2009-5-16 12:24:37

1阶就是骰子。。。。。。

作者: Ricky.C 时间: 2009-5-16 13:38:13

原帖由 bardy 于 2009-5-16 12:13 发表

呵呵，我是想找一下详细的研究。以科学的态度

我看很多人可以学习一下，怎样把一件事情说得清楚明白

科学要怎么做，学问要怎么做。该详细的时候还是需要详细的

\\

說到要比賽.

1x1x1 的比賽真的有意義嗎?

只不過一個笑話

作者: bardy 时间: 2009-5-16 14:05:13

原帖由 CTS 于 2009-5-16 13:38 发表
...
只不過一個笑話

没有幽默细胞的话很多笑话都理解不了

作者: iPhoenix 时间: 2009-5-16 14:54:27

这东西还有轴吗？？

作者: yq_118 时间: 2009-5-16 15:37:44

（-1）×0×（1）的最好玩，

作者: mops 时间: 2009-5-16 17:41:47

1X1X1的比赛,,其实也是手速的比赛..看谁按计数器快..那个对计数器的要求要多几个小数点才能分出胜负了.

作者: lily748 时间: 2009-5-16 20:59:27

这张照片真的好看吖，LZ厉害

作者: wh6816 时间: 2009-5-17 00:43:02

单个一个块不知算不算是一阶啊。。。

作者: xiaofeng206 时间: 2009-5-17 01:02:17

一阶的估计只能是个摆设，不用拼就好了啊

作者: mag_kummel 时间: 2009-5-17 01:23:19

那个叫做骰子.
以上

作者: 赵世主 时间: 2009-5-17 12:54:36

1阶魔方的24种状态，雷！
好多英文啊~~

作者: kexin_xiao 时间: 2009-5-17 14:19:25

3楼好多魔方啊

作者: zqp2009 时间: 2009-5-17 14:43:42

一阶怎么还原？
不用还原吧~~~~~~~~

作者: sy1807 时间: 2009-5-17 16:38:22

额。。。。。。。。。。。。。牛啊！！！！！！！！！！！！！！！！！！！！！！！！！！

作者: JunwenYao 时间: 2009-5-18 11:20:50

问，楼主的LOGO是什么材料的？找厂做的还是自己做得？如何做得？帮忙解答.

因为最近我们俱乐部的魔友，想做LOGO，我手上有很多方案……但是希望听听专业人士的意见。

作者: 逍遥0 时间: 2009-5-18 14:06:26

打麻将时用的色子是不是也应该算是一阶魔方呢？？

作者: bardy 时间: 2009-5-18 18:20:47

原帖由 逍遥0 于 2009-5-18 14:06 发表
打麻将时用的色子是不是也应该算是一阶魔方呢？？

差不多吧

相当于是有中心块图案方向的一阶魔方了

作者: Vicki 时间: 2009-5-18 18:25:26

看来很多人以为我是LZ~

看清楚3楼那张图是我的没错~

但是我不是LZ~

作者: 无限正义 时间: 2009-5-18 18:25:51

1X1X1，又不能拧，有什么意思？

作者: flwb 时间: 2009-5-18 18:32:29

应该叫一阶方块,怎么能叫魔方?

作者: 肥熊 时间: 2009-5-18 18:40:11

這個不難吧..
這個骰子貼上貼紙就是了..

作者: 604222420 时间: 2009-5-18 18:40:14

那么好，它唯一的一个块有6个面，它该如何命名，如何确定“打乱”状态，说白了，1阶魔方的意义何在？

作者: snowchou 时间: 2009-5-18 20:26:50

做过N个1阶钥匙链，都是山寨圣恩角块做的，效果不错，可惜没黑色的。

建议把该文转到英文资料区。

作者: wuchenfei 时间: 2009-5-18 20:29:55

那是筛子......

作者: sjont 时间: 2009-5-19 08:00:13

提示: 作者被禁止或删除内容自动屏蔽

作者: bardy 时间: 2009-5-19 09:06:21

原帖由 snowchou 于 2009-5-18 20:26 发表
...

建议把该文转到英文资料区。

你可以认为这是我从英文资料区里找出来的

没人看的东西先扔在英文资料区里面，然后有人读过之后从中找一些出来讨论一下，理解一下，是这个流程吧？

作者: bardy 时间: 2009-5-19 09:07:11

原帖由 sjont 于 2009-5-19 08:00 发表
...
外国人的思维都是比较理性的~~
...

就是啊有些人不但不够理性幽默细胞也不够

作者: cyz 时间: 2009-5-19 18:11:15

在魔方比赛中完成后是不会计较朝向问题的，所以一阶没有必要存在

作者: hfyxin 时间: 2009-5-19 19:27:01

有意思，继续推广到0x0x0呢？

作者: bardy 时间: 2009-5-20 11:44:33

原帖由 cyz 于 2009-5-19 18:11 发表
在魔方比赛中完成后是不会计较朝向问题的，所以一阶没有必要存在

要区别对待。规定是人做出来的。

你所说的魔方比赛应该不包括一阶。如果真的要来个一阶的魔方比赛的话，规定肯定要另外制定了

作者: 604222420 时间: 2009-5-20 17:28:53

好吧，根本上来说，1X1X1不算做魔方，至于理论乌木大烟头等人都说过。所以这种东西需要重新定名，至少不是魔方。

作者: beijiaoff 时间: 2009-5-21 08:30:05

我也有这种1阶
收藏。显摆用

作者: 塞翁 时间: 2009-5-21 08:53:38

一阶不是用来玩的。
它可以是一个研究对象，也可以是一个饰物。

作者: bardy 时间: 2009-5-21 17:04:17

原帖由塞翁于 2009-5-21 08:53 发表
...
它可以是一个研究对象，也可以是一个饰物。

这倒是说得有道理，非常理性啊

作者: ducksun5555 时间: 2009-5-21 17:14:27

1*1*1是个方块，还原也就是朝向问题，只要是个正常人都可以简单的还原，谈不上魔方吧。魔方的魅力就在于既是是个二阶的，也没那么容易还原.....其实比三阶的也没容易到哪去

作者: 06154 时间: 2009-5-22 11:57:38

111还能算是魔方吗？？骰子算不算是？？

作者: 无为子 时间: 2009-5-22 13:14:51

这个魔方好做，谁都好做，一个小方块

作者: lamianbu 时间: 2009-5-22 20:12:24

原帖由 Vicki 于 2009-5-16 11:08 发表
其实一阶严格来说不能算是魔方~

乌木还是大烟头说过：有相交的旋转面才能称作魔方~

所以最简单的魔方是1x2x2~

http://bbs.mf8-china.com/viewthread.php?tid=28193

还有更简单的。

1x1x2

作者: 小小鬼 时间: 2009-5-23 09:21:19

呵呵..我原来看到一个Snowchou做过一个..~~

作者: qqkokoyoyo 时间: 2009-6-1 16:36:26

真羡慕3楼的

作者: yq_118 时间: 2009-6-1 16:56:38

还真有无聊的人啊，这个要是能盲拧就好了

作者: Cheng_943 时间: 2009-12-27 16:50:25

这有意思么... ....

作者: 柯哀之恋 时间: 2017-3-26 23:28:57

1阶就一种状态，还能打乱不成

作者: 秘仪 时间: 2017-5-10 21:34:21

那就是个骰子。骰子不是魔方。破事水。

作者: LSeng 时间: 2017-5-21 02:07:38

加贴纸的骰子

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