小菜魔神
发表于 2006-8-13 17:28:13
<font size="5">魔方</font><font size="3">是由<font color="#0000ff"><b>匈牙利</b></font> 布达佩斯商用艺术学校教师<font color="#0000ff"><b>鲁比克</b></font>发明的,目的是为了增强学生的三维空间想象能力。<br/> <font size="5"> 魔方</font><font size="3">是一个正方体,每个面由9个小方块组成,同一面的每个小方块上都涂上同一种颜色,一共是6种颜色,转动这些小方块竟能组成 8!×3<sup>7</sup>×12!×2<sup>10</sup> =43,252,003,274,489,856,000 ≈4×10<sup>19</sup></font>种不同的颜色组合图案!大约为4000亿亿种。 <p>为了便于描述及记忆,我们定义一下魔方各个方块的名称:<br/> <font color="#ff0000">角方块:</font>8个顶角上的方块,每个方块只看到3面,有3种不同颜色;<br/> <font color="#ff0000">棱方块:</font>两个角方块之间的方块,整个魔方有12条棱故共有12个棱方块,每个方块只看到2个面,有2两种颜色;<br/> <font color="#ff0000">中方块:</font>每个面中央的方块,它只露出一面。<br/>我们再分析一下上面的计算:<br/>8!(8个角方块可能有8个位置) ×3<sup>7</sup>(8个角方块各有3种不同的颜色朝向,注意不是3<sup>8</sup>,因为决定了7个角方块方向后,第8个角方块的方向也就固定) ×12!(12个梭方块各有12个可能的位置,但11个梭方块也决定第12块的位置,故应为12!×1/2) ×2<sup>10</sup>(12个梭方块各有2个不同颜色朝向,同样11个梭方块的方向也决定 了第12个梭方块的方向,故为2<sup>11</sup>)。 </p><p> <font size="5"> 1974</font><font size="3">年夏天,<font color="#0000ff"><b>鲁比克</b></font> 成功地设计了这个机械装置,在兴奋之余随意旋转几下小方块,却发现被扭乱了的立方体无法还原。后来他花了几个星期的时间去研究各小方块之间的位置关系才恢复原状。</font></p></font>
乌木
发表于 2006-8-13 20:29:21
<p><font face="宋体"><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">先要固定六个中心块的相对位置及绝对位置都不变,即对于魔方花样无贡献,再讨论角和棱的各种可能状态。</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><p></p></span></font></p><p><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个角方块可能有</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个位置。--</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">!</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"> </span><font face="宋体"><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">;</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><p></p></span></font></p><p><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个角方块各有</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">3</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">种不同的颜色朝向,注意不是</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">3<sup>8</sup></span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">,因为决定了</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">7</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个角方块方向后,第</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个角方块的方向就仅有一种可能了(否则魔方无法复原的)。--</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">3<sup>7 </sup></span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">。</font></span><span style="FONT-FAMILY: "Times New Roman";">
<span lang="EN-US"><p></p></span></span></p><p><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个棱方块可能有</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个位置。--</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">!</font></span><span style="FONT-FAMILY: "Times New Roman";">
</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">;(</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">110</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">楼说法有误,不能说</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">“11</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个棱方块也决定第</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">块的位置,故应为</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12!×1/<chmetcnv wst="on" tcsc="0" numbertype="1" negative="False" hasspace="False" sourcevalue="2" unitname="”">2”</chmetcnv></span><font face="宋体"><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">)</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><p></p></span></font></p><p><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个棱方块各有</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">种不同的颜色朝向,注意不是</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">2<sup>12 </sup></span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">,因为决定了</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">11</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个棱方块方向后,第</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><font face="宋体">个棱方块的方向就仅有一种可能了(否则魔方无法复原的)。--</font></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">2<sup>11 </sup></span><font face="宋体"><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">。</span></font></p><p><font face="宋体"><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";"><strong> 待续</strong></span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><p></p></span></font></p>
[此贴子已经被作者于2006-8-13 20:50:36编辑过]
乌木
发表于 2006-8-13 20:52:35
<p><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><strong>8!×3<sup>7</sup>×12!×2<sup>11 </sup>/ 2</strong>
</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,这除以</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">是因为什么?不会是</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">110</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">楼说的原因,我认为是:</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!种角态中有</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/ 2 </span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">个属于</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">“</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">扰动态</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">”</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,另</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/ 2 </span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">个为非扰动态。同理,</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/ 2 </span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">个扰动态棱,</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/ 2 </span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">个非扰动态棱。扰动态角花样只能配扰动态棱花样,非扰动角花样只能配非扰动棱花样。所以,由于角和棱位置不同而引起的花样数为(</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">)</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">×</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">(</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">)+(</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">)</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">×</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">(</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">)=</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">8</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">×12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">!</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">/2 </span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">。即,这除以</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">2</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">与</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">“11</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">个棱方块也决定第</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">12</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">块的位置</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">”</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">无涉。(关于</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">“</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">扰动</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">”</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,请见理论区</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";">pengw</span><span style="mso-bidi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">的文章。)</span><span lang="EN-US" style="FONT-FAMILY: "Times New Roman";"><p></p></span></p>
虫舂
发表于 2006-8-13 21:11:28
很多图片看不了
10473059
发表于 2006-8-14 10:50:49
我看得是糊里糊涂啊~~~~~学不会了,学不会了~~~
10473059
发表于 2006-8-14 12:23:22
我一上午终于拼出一面了~~~~55~~~多么不容易啊,可是旁边好乱,这样拼法是不是错误的?
10473059
发表于 2006-8-14 12:28:18
<p>要完成其它的面,那岂不是要打乱已经拼好的??</p>
jasonyang
发表于 2006-8-14 13:10:14
<p>a)如图 9 <img src="http://www.puzzlesolver.com/data/29/images/step5-4.gif" alt=""/> 做<b>R'U2RUR'UR</b>
<br/>b)如图10 <img src="http://www.puzzlesolver.com/data/29/images/step5-5.gif" alt=""/> 做<b>R'U'RU'R'U2R</b>
<br/>c)如图11 <img src="http://www.puzzlesolver.com/data/29/images/step5-6.gif" alt=""/> 做<b>UR'U2RUR'UR </b><br/>d)如图12 <img src="http://www.puzzlesolver.com/data/29/images/step5-7.gif" alt=""/> 做 <b>R'U2RUR'URU'R'U2RUR'UR</b>
</p><p>按照公式达不到图示的目的?</p>
乌木
发表于 2006-8-14 15:13:23
回116楼,第1面好不算好,要第1层好(见下面java图,用鼠标拖着可转动过来看背面),接着复原第2层和第3层,祝你成功! <applet codebase="3" height="200" width="200" code="RubikPlayer.class"><param value="SupersetENG" name="scrptLanguage"/><param value="0,0,0,6,0,6,6,6,6" name="stickersFront"/><param value="1,1,1,6,1,6,6,6,6" name="stickersRight"/><param value="6,6,6,6,2,6,6,6,6" name="stickersDown"/><param value="3,3,3,6,3,6,6,6,6" name="stickersBack"/><param value="4,4,4,6,4,6,6,6,6" name="stickersLeft"/></applet>
乌木
发表于 2006-8-14 15:24:40
回117楼,按照公式完全可实现图示要求,您再试试。仅看棱,不管角,图是顶视图(俯视图),即做操作“U”时,蓝色中心块转动!