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魔方理论探索者 论坛建设奖 爱心大使 十年元老

11#
发表于 2008-8-26 17:29:47 |只看该作者
1楼内容更新后,条件更苛刻了,只转两个面之外,还要不翻色邻块互换啊!此题蛮难的,不管答案是肯定的还是否定的,都得有理论指点啊。

[ 本帖最后由 乌木 于 2008-8-26 17:32 编辑 ]

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论坛建设奖 爱心大使 八年元老

12#
发表于 2008-8-27 10:02:04 |只看该作者
乌木老师都迷糊了,我就不想了,有差距,呵呵
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魔方理论探索者 八年元老

13#
发表于 2008-8-27 10:09:30 |只看该作者
N阶定律讨论的变换是指公式的结果而不是公式自身,N阶定律对一个结果是选用什么公式来实现好像并不在乎,只对可能产生什么样的结果感兴趣,所以我以不知道如果回答啊,这个问题可能还是要研究最小步的大师来回答

[ 本帖最后由 pengw 于 2008-8-27 10:12 编辑 ]

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魔方理论探索者 八年元老

14#
发表于 2008-8-27 11:19:08 |只看该作者

替代最小步大师试着分析一下

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< class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman" color=#000000 size=3>1</FONT></SPAN></P></TD>
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<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US>ffice<IMG alt= src="http://bbs.mf8-china.com/images/smilies/default/shocked.gif" border=0 smilieid="6">ffice" /&gt;<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o:p><FONT face="Times New Roman" color=#000000>&nbsp;</FONT></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN lang=EN-US><FONT face="Times New Roman">A</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行代表复原状态的</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">个块,其中</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">2</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">3</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">4</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">位于同一层,称为上层。</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">、</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">位于下层</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN lang=EN-US><FONT face="Times New Roman">B</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行代表向右的一次四元置换,生成四元环(</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">4</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">2</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">3</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">),显然靠上层转动是完法形成单一二元环</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN lang=EN-US><FONT face="Times New Roman">C</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行引入底层二个块</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">、</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">到上层,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">B</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行的</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">2</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">进行一次向左的四元置换,</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN lang=EN-US><FONT face="Times New Roman">D</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">C</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行的</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">4</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">进行一次向右的四元置换,最终生成独立二园环(</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">4</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">3</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">)</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"><FONT color=#000000>说明:</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">以上的二元置换不计相似变换步数,至少也要三步,事实上是不可能的。然而,在第</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">C</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行将</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">调入上层已动到侧层,而</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">C</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">行的置换顺序是</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">2</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">实际上是</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5,6,2,1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">,要调整这个顺序,必须动用底层,由此二底加一侧都动了,即楼主所说的三面至少动一次。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"></SPAN></FONT>&nbsp;</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"></SPAN></FONT>&nbsp;</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">------------</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"></SPAN></FONT>&nbsp;</P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT color=#000000><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">注意,不基于最基本的四元置换去求证任何置换,在逻辑上都是站不脚的</SPAN></FONT></P>

[ 本帖最后由 pengw 于 2008-8-27 11:27 编辑 ]

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透魔

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15#
发表于 2008-8-27 22:33:55 |只看该作者
大家通过魔方研究的东西悦来月广了,
一切从“零”开始。

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红魔

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六年元老

16#
发表于 2008-8-28 07:08:44 |只看该作者
<P>我想到可以用穷举法解决 呵呵</P>
<P>&nbsp;</P>

[ 本帖最后由 Atato 于 2008-9-6 18:10 编辑 ]
如果最初的想法不是荒谬的, 那么它就毫无希望.
                                                                      -阿尔伯特·爱因斯坦

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魔方理论探索者 八年元老

17#
发表于 2008-8-28 09:11:44 |只看该作者
对于一个给定变换,尚没有一种统一简单的办法,用来找出一个更短的公式,先不要说最短的公式,当前的方法就是穷举.我上面的做法还算不上穷举

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发表于 2008-8-28 10:12:39 |只看该作者
对 忍大师上面的方法只是用了轮换而已.
如果最初的想法不是荒谬的, 那么它就毫无希望.
                                                                      -阿尔伯特·爱因斯坦

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19#
发表于 2008-8-28 10:19:10 |只看该作者
呵呵,大师证出来了哈............强悍
原来死神还不想完结。。。。。

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发表于 2008-8-28 10:20:24 |只看该作者
事实上,每一转都是四轮换,四轮换是一切置换的构造基础

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