锁具装箱问题的数学模型

锁具装箱问题的数学模型
詹国武 1 黄景文 1 周辉莉 2
（1.05级化工系； 2.05级经济系）
摘要：本文针对锁具如何装箱问题，建立了一个新模型，并对其进行了分析和评价。

就如何装箱问题，本文建立了一个如何对每一批锁具进行装箱和标记才能是消费者的满意度最高的模型，再具体分析实际销售情况，建立了在消费量不同情况下，如何组合已装箱好的锁具才能使满意度最大的模型以及，再对此模型进一步探讨和分析，得到一个当销售箱数超过49箱仅仅用同奇或者同偶类的锁具来组合的模型,并且对其进行了论证,最终得到最优的结果利用软件通过筛法，分别求得一批锁具钥匙的槽高由3个，4个，5个不同数组成的个数为2544，2808，528，一批锁具的个数和箱数5880和98。

再根据能够互开的锁具的条件，且根据槽高为连续的整数特性，得到结论：当一个钥匙的槽高之和为奇（偶）时，他的互开钥匙的槽高和必为偶（奇），即槽高和同为奇（偶）的必不能互开，得到把奇偶分开装箱和标记的一个初步方案，为了定量的分析不同的方案，利用概率论的方法，引入了平均互开对的概念。

对于随后的销售方案，我们利用图论知识，从最小匹配数入手，通过对平均互开对数的大小比较来衡量各个方案和组合的最优情况，得到如下结论，当销售不超过49箱时，只销售槽高和为奇（偶）的，当超过49箱时则按下问所论述的搭配方案，再进一步打破陈规，当按下文的装箱和标记，仅仅销售奇（偶），能够使抱怨的程度更小。

关键词：筛法奇偶分箱同奇或同偶销售平均对开数顾客抱怨度最小匹配
一．问题的重述
某厂生产一种弹子锁具，每个锁具的钥匙有5个槽，每个槽的高度从｛1，2，3，4，5，6｝6个数中任意的取一数，但对于每个钥匙的5个槽高的取值需要满足以下两个条件
1．至少有3个不同的数
2．相邻的两槽的高度差不能为5
满足以上两个条件的所有不同的锁具称为一批，销售部门随意的取60个装一箱出售
同一批锁可以互开的条件：
1.二者相对应的5个槽的高度中有4个相同
2.另一个槽的高度相差为1
由于销售部门随意的取60个装一箱，所以同一消费者可能买到互开的锁具，导致了消
费者的不满。

我们的问题如下：
1．每一批锁具有多少个，能装多少箱？
2．求下面三个事件的概率：
（1）槽的高度由5个不同数字组成；
（2）槽的高度由4个不同数字组成；
（3）槽的高度由3个不同数字组成。

3.销售部门如何制定一个方案，包括如何装箱（仍旧是60个锁具装一箱），如何给箱子以标记，出售时如何利用这些标志，是团体顾客不再抱怨或者减少抱怨。

二．问题的分析
本题目是要求求出一批锁具的个数和装箱数，以及槽的高度由5个，4个，3个不同数字组成的概率，由于这个问题的数据量比较小，对于这个可以用mathematic和matlab 处理软件利用筛法，直接求出，。

我们从奇偶性出发，利用奇偶分类的思想和图论的最小匹配知识，寻找各个锁具的最小匹配数，发现在大于49箱时，奇类和偶类的匹配数都一样，从这里入手，我们建立了自己的模型。

同时，团体购买的消费者对产品的抱怨来自于锁之间的互开程度。

于是，我们引入互开数的概念，通过互开率来进行对费者抱怨度的分析，来评价每个模型。

三．模型假设
1．可以生产槽高精确的锁具
2．生产过程中可以对每个槽高进行控制，即按所安排的不同锁具排列顺序生产并且可以更改设置
3．能够以上锁具互开条件的一定能够互开
4.互开对的百分比与顾客不不满意度成正比,在这里不妨设其相等
四．符号及概念的说明
n:一批锁具中槽的高度由5个不同的数字组成的锁具个数.
5
n:一批锁具中槽的高度由4个不同的数组成的锁具个数
4
n:一批锁具中槽的高度由3个不同的数组成的锁具个数
3
N：一批锁具的总个数
M：一批锁具的箱数
n/N
P5：
5
n/N
P4：
4
n/N
P3：
3
h:第i个槽的高度
i
H:5个槽高的和
No ：一批锁具中H 为奇数的个数
Ne:一批锁具中H 为偶数的个数
Ho M :一批锁具中H 为奇数的装箱数
He M :一批锁具中H 为偶数的装箱数
互开对:能够互开的锁具的对数
五．模型的建立与求解
1．对本题题目中问题的求解
利用mathematic 和matlab 求得：
总数：N=5880
M=98
5n =528
4n =2808
3n =2544
从而求得：P 5=528÷5880=89.8‰
P 4=2808÷5880=477.6‰
P 3=2544÷5880=432.6‰
2．装箱方案
（1）．对问题进行具体的分析，找到途径
对于本题目所给的数据进行分析，槽的高度选择为一连续整数列，想到某个钥匙的H 为一奇数（偶数）时，则其互开钥匙的H 必为大1或小1的偶数（奇数），这样我们把H 为奇数的分成一个集合O,H 为偶数的分为一个集合E ，这样，同属于O （E ）的之间则一定不能互开，当在奇数集O 中任意加入一个H 为偶数的keyl 形成新的集合O ',因为keyl 在O 中一定有与其互开的锁，所以O '元素之间不再为必不互开了，所以奇数集合O （或偶数集合E ）即为任意两个元素之间必不互开的最大集合。

这里通过把锁局具进行分类成为O 和E ，然后分开装箱和分开销售，就可以尽量的避免互开的现象。

（2）．对H 为奇数和偶数的锁具个数的求解
设12345l l l l l 为任一符合规格的锁具的槽高排列
令 :在O 中锁具S=12345l l l l l ,与它互补的一锁具为12345(7)(7)(7)(7)(7)l l l l l ----- 因为:1234512345()(77777)l l l l l l l l l l +++++-+-+-+-+-=35
且假设:12345l l l l l ++++为奇数
所以: 1234577777l l l l l -+-+-+-+-为偶数
又因为:16i l ≤≤且15i i l l ±-<
所以有:176i l ≤-≤且111(7)(7)5i i i i i i l l l l l l ±±±---=-=-<
得出任一O 中所对应的互补锁具都符合要求:
所以有: No ≤ Ne
同理可得: Ne ≤ No
最终得到结果: Ne= No=5880/2=2940(此结论也同时用mathematic 和matlab 进行了验证)
所以:Ho M =He M =98/2=49
（3）.装箱和标记
为了将H 为奇数的和H 为偶数的区分开,应用不同的标记来表示箱子如标上“奇”，“偶”不同字样,为了让区别更叫明显也可以对装不同奇偶性锁具的箱子用不同的颜色制成,为了使单个锁也能区分其奇偶性,可以把标记做在锁具上,这样即使箱子损坏或没有箱子时也能区分其奇偶性,当销售不超过49箱时,只销售Ho M 或He M 中的锁具则可实现锁具不能互开的要求,但这里要求出售的是同一批的产品,当锁具有囤积的时候就难以区分是否是同一批,所以每一批也应该明显的标志出生产批号.
3. 对以上模型的优化
由于在实际销售过程中往往可能大于49箱,当超过49箱后我们应该怎样组合才能使互开的几率更小呢
对同一批所生产的锁具进行两两对比,看是否能够互开,得到能够互开的对数.此目的可以用mathematica 和matlab 来实现,
得到的结果为:
U=22778(对)
则平均每个锁具能组成的互开的对数:u =22778/(5880/2)=7.75(对)
A.对于随机装箱的分析
在一箱中,对于任一锁具S,与其成互开对的平均个数为: 1u =59(58801)
u -=0.078(个) 整箱所对应的互开对为:
1u =1u 602
=2.33(对)
利用上面的模型推广到更为普遍的k 箱
则有: k u =u 6015879
k - k u =602k k u =22778(601)587998
k k ⨯⨯-⨯ 上面的公式对k *N ∈都适用
B.对奇偶分开装箱的分析
当购买量不超过49箱时,不会出现互开的情况,这时i u (149i u ≤≤)=0.当购买超过49箱时,则先从奇(偶)类中抽出49箱,再从偶(奇)类中抽出k-49箱,在前面的49箱和后面的k-49箱的锁之间才能构成互开关系,所以有k 箱锁具中的平均互开对数为: 60(49)k
u u k '=⨯-=7.75×60×( k-49)=465k-22785 得到在互开次数的分段函数:
0(049)46522785(4998)k k u k k ≤≤⎧'=⎨-≤⎩
C.对此模型的改进:
由于不同的锁具其互开对数时不一样的,（比如对于每个偶类的锁，他们能在奇类的锁中找到的互开的锁的数量是不相同的），我们当然希望能够将偶（奇）类的锁具按照它们能够在奇（偶）类的锁中找到互开的锁的多少进行分类,在卖完一类49箱后，先将另一类中有互开次数少的先卖，在卖有互开次数多的锁，所以得到方案。

这里用mathmatic 处理得到各个锁具互开对数以下结果
有4个互开对数的共有45个,其分别是:
{1,1,1,2,3},{1,1,1,3,2},{1,1,1,5,4},{1,1,1,5,6},{1,1,2,1,3},{1,1,2,3,1},{1,1,3,1,2},{1,1,3,2,1},{1,1,4,1,5},{1,1,4,5,1},{1,1,5,1,4},{1,1,5,4,1},{1,2,1,1,3},{1,2,1,3,1},{1,2,3,1,1},{1,3,1,1,2},{1,3,1,2,1},{1,3,2,1,1},{1,4,1,1,5},{1,4,1,5,1},{1,4,5,1,1},{1,5,1,1,4},{1,5,1,4,1},{1,5,1,5,6},{1,5,4,1,1},{1,5,6,5,1},{2,1,1,1,3},{2,1,1,3,1},{2,1,3,1,1},{2,3,1,1,1},{3,1,1,1,2},{3,1,1,2,1},{3,1,2,1,1},{3,2,1,1,1},{4,1,1,1,5},{4,1,1,5,1},{4,1,5,1,1},{4,5,1,1,1},{5,1,1,1,4},{5,1,1,4,1},{5,1,1,5,6},{5,1,4,1,1},{6,5,1,1,1},{6,5,1,1,5},{6,5,1,5,1}}
有5个互开对数的共有105个,其分别为:
{{1,1,1,3,4},{1,1,1,4,3},{1,1,1,4,5},{1,1,1,5,2},{1,1,2,1,5},{1,1,2,5,1},{1,1,2,6,2},{1,1,2,6,6},{1,1,3,1,4},{1,1,3,4,1},{1,1,4,1,3},{1,1,4,3,1},{1,1,5,1,2},{1,1,5,2,1},{1,1,5,5,6},{1,1,5,6,5},{1,2,1,1,5},{1,2,1,5,1},{1,2,5,1,1},{1,2,5,1,5},{1,2,6,2,1},{1,3,1,1,4},{1,3,1,4,1},{1,3,4,1,1},{1,4,1,1,3},{1,4,1,3,1},{1,4,3,1,1},{1,4,5,1,5},{1,5,1,1,2},{1,5,1,2,1},{1,5,1,5,2},{1,5,1,5,4},{1,5,2,1,1},{1,5,2,1,5},{1,5,2,5,1},{1,5,4,1,5},{1,5,4,5,1},{1,5,5,1,2},{1,5,5,1,4},{1,5,6,6,6},{2,1,1,1,5},{2,1,1,5,1},{2,1,5,1,1},{2,1,5,1,5},{2,1,5,5,1},{2,5,1,1,1},{2,5,1,1,5},{2,5,1,5,1},{2,5,1,5,5},{2,5,5,1,5},{2,6,2,1,1},{3,1,1,1,4},{3,1,1,4,1},{3,1,4,1,1},{3,4,1,1,1},{4,1,1,1,3},{4,1,1,3,1},{4,1,3,1,1},{4,1,5,1,5},{4,1,5,5,1},{4,3,1,1,1},{4,5,1,1,5},{4,5,1,5,1},{5,1,1,1,2},{5,1,1,2,1},{5,1,1,5,2},{5,1,1,5,4},{5,1,2,1,1},{5,1,2,1,5},{5,1,2,5,1},{5,1,4,1,5},{5,1,4,5,1},{5,1,5,1,2},{5,1,5,1,4},{5,1,5,2,1},{5,1,5,2,5},{5,1,5,4,1},{5,1,5,5,2},{5,1,5,5,6},{5,1,5,6,5},{5,2,5,1,5},{5,4,1,1,1},{5,5,1,5,2},{5,5,1,5,6},{5,6,5,1,1},{5,6,5,1,5},{6,5,1,5,5},{6,5,5,1,1},{6,5,5,1,5},{6,6,2,1,1},{6,6,6,5,1},{1,5,2,6,2},{1,5,2,6,6},{1,5,6,2,6},{1,5,6,6,2},{2,6,2,1,5},{2,6,2,5,1},{2,6,6,5,1},{5,1,2,6,2},{5,1,2,6,6},{6,2,1,5,6},{6,2,6,5,1},{6,5,1,2,6},{6,6,2,1,5},{6,6,2,5,1}}
有6个互开对数的有296个(在这里就不详尽列出来,可考察附录)；
有7个互开对数的有699个(在这里就不详尽列出来,可考察附录)；
有8个互开对数的有901个(在这里就不详尽列出来,可考察附录)；
有9个互开对数的有744个(在这里就不详尽列出来,可考察附录)；
有10个互开对数的有105个(在这里就不详尽列出来,可考察附录)；
从这里可以看出,我们可以任意选择奇(偶)作为前面的49箱(本题选择了奇),对此奇(偶)类的生产可以不必加以排序,随即生产即可,但若要能够使后面的匹配得以实现,则不仅仅要区别出奇偶性,还要区别产品的生产顺序号,在这里之所以列出每个锁具对应的槽高数列,是为了方便安排生产,使生产按照互开对数增加的序列方向进行，然后从有互开次数少的锁开始装箱，比如将45个有4个互开次数的锁和15个有5个互开次数的锁装一箱，要把有5个互开次数的锁放箱子底边，表示有4个互开次数的锁先卖，依此类推。

如果生产过程服从上面所得的数据的排列顺序则可以很明确的知道何时生产何等级的锁具,然后对不同等级的锁具箱子或直接锁具上做好明确的标记,使搭配可以顺利准确的进行
所以得到这种方法的互开次数，如下的分段函数:
00k <= 49460(k - 49)(49 <k<= 49 + 45/60)445 + 560(k - 49 - 45/60)(49 + 45/60<k<= 49 + 150/60)445 + 5105 + 660(k - 49 - 150/60)
(49 + 150/60<k <= 49 + 446/60)445 + 5105 + 6296 + 760(k u ≤⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯''=k - 49 - 446/60)(49 + 446/60<k <= 49 + 1145/60)445 + 5105 + 6296 + 7699 + 860(k - 49 - 1145/60) (49 + 1145/60<k <= 49 + 2046/60)445 + 5105 + 6296 + 7699 + 8901 + 960(k - 49 - ⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯2046/60) (49 + 2046/60<k <= 49 + 2790/60)
445 + 5105 + 6296 + 7699 + 8901 + 9744 + 1060(k - 49 - 2940/60)(49 + 2790/60<k <= 49 + 2940/60)⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⨯⨯⨯⨯⨯⨯⨯⨯⎪⎪⎩
D.消费量超过49箱时,多出的用同奇偶性的锁具补充的模型
由于同为奇(偶)类的锁具,它们能够互开的条件是：必须是相同的锁
当k<=49时, k
u '''=0 当49<k<=98时,由于在原有的49箱中,每个奇(偶)的模型都有了,所以每增加一个锁
具,则其互开对数增加一个,得到k
u '''=60(k-49) 联合上面的,得到: 0(049)60(49)(4998)k k u k k <≤⎧'''=⎨-<≤⎩
为了更直观的比较四种方案,用mathematic 画出了以上四种模型互开次数与箱数函数
其中：f1为随机装箱的互开对数与箱数函数；
f2为奇偶分开装箱互开对数与箱数函数；
f3为奇偶分开装箱又按具有互开对数多少分类的互开对数与箱数函数； f4为都卖同一类锁（奇或偶）互开对数与箱数函数。

由上可以看出用第四中方案所产生的互开对数会比较少，而顾客买同样的多的锁产生的互开次数越多顾客的不满意度会增加。

所以当同一客户买的锁不超过98箱时，以第四中方案卖锁最好。

这里我们只稍微对其做下简单的解释：对于奇偶交叉卖：同一客户，当买完49箱奇（或偶）时，每卖一个偶（或奇）的锁是都会加至少4个互开对数；而对与只卖奇（或偶）型的锁时，当卖完49箱时，每多卖一个奇（或偶）型锁都只加一个互开对数，所以这个方案来的比较优。

当同一客户买的所超过98箱的情况，同理我们可推出当客户买的锁大于98时，买同一种类型的锁会来的好。

六.模型的评价与改进
1.我们所研究的是针对一个客户的策略，本模型对于这个有较优的适用性，具有一定的实际意义和参考性。

2.在我们的模型假设中我们认为顾客的抱怨度和互开对百分比相等，但是当模型的基数极大的时候，无疑这个假设是有一定误差的。

这个是值得进一步改进并加以推广的。

3．模型在不忽略整体的情况下，从个体出发进行分析，避免了陷入整体情况的讨论。

同时又能反映整体情况。

七.参考文献
[1] 全国大学生数学建模竞赛委员会，《全国大学生数学建模竞赛优秀论文汇编》，北京：中国物价出版社，2002
[2] 王树禾，《图论》，北京：科学出版社，2004 20406080100箱
500010000
15000
20000
互开次数
f1f2
f3
f4
[3] 朱道元，《数学建模案例精选》，北京：科学出版社，2003
八、附录
以下部分是本模型主要代码：
Clear["Global`*"]
a=Table[{i,j,k,l,m},{i,1,6},{j,1,6},{k,1,6},{l,1,6},{m,1,6}]; b=Flatten[a,4];
p1=Length[Union[#1]] 3&;
p2=Length[Union[#1]] 4&;
p3=Length[Union[#1]] 5&;
Table[c[i]=0,{i,1,3}];
c[1]=Select[b,p1];
c[2]=Select[b,p2];
c[3]=Select[b,p3];
For[i=1,i≤3,i++,d[i]=DeleteCases[DeleteCases[c[i],{___,1,6,___} ],{___,6,1,___}]];
n1=Length[d[1]]
n2=Length[d[2]]
n3=Length[d[3]]
n=n1+n2+n3
m=n/60
g=Join[d[1],d[2],d[3]]
2544
2808
528
5880
98
由于5880种锁，数据太大，这里就不不输出，有意者可以将上面程序在mathematica中运行。

(*o,e分别为奇数和偶数锁具*)
o=Select[g,OddQ[Plus@@#]&]
e=Select[g,EvenQ[Plus@@#]&]
Length[o]
Length[e]
2940
2940
这里也没给出o和e，有意者可运行上面程序。

(*t为锁的可以互开数,我们叫为匹配数*)
t=0;
For[i=1,i≤5880,i++,For[j=1,j≤5880,j++,If[Sort[g[[i]]-g[[j]]] {0 ,0,0,0,1},t++]]];
t
22778
Table[w[i]=0,{i,1,2940}];
For[i=1,i≤2940,i++,For[j=1,j≤2940,j++,If[Sort[Abs[o[[j]]-e[[i]] ]] {0,0,0,0,1},w[i]++]]];
s=Table[w[i],{i,1,2940}];Table[p[i]=Position[s,i],{i,4,10}];Fo
r[i=4,i≤10,i++,u[i]=Extract[e,p[i]];Print["有",i,"个匹配数,总共",Length[p[i]],".如下:"];Print[u[i]]]
有 4 个匹配数,总共 45 .如下:
{{1,1,1,2,3},{1,1,1,3,2},{1,1,1,5,4},{1,1,1,5,6},{1,1,2,1,3},{ 1,1,2,3,1},{1,1,3,1,2},{1,1,3,2,1},{1,1,4,1,5},{1,1,4,5,1},{1, 1,5,1,4},{1,1,5,4,1},{1,2,1,1,3},{1,2,1,3,1},{1,2,3,1,1},{1,3, 1,1,2},{1,3,1,2,1},{1,3,2,1,1},{1,4,1,1,5},{1,4,1,5,1},{1,4,5, 1,1},{1,5,1,1,4},{1,5,1,4,1},{1,5,1,5,6},{1,5,4,1,1},{1,5,6,5, 1},{2,1,1,1,3},{2,1,1,3,1},{2,1,3,1,1},{2,3,1,1,1},{3,1,1,1,2} ,{3,1,1,2,1},{3,1,2,1,1},{3,2,1,1,1},{4,1,1,1,5},{4,1,1,5,1},{ 4,1,5,1,1},{4,5,1,1,1},{5,1,1,1,4},{5,1,1,4,1},{5,1,1,5,6},{5, 1,4,1,1},{6,5,1,1,1},{6,5,1,1,5},{6,5,1,5,1}}
有 5 个匹配数,总共 105 .如下:
{{1,1,1,3,4},{1,1,1,4,3},{1,1,1,4,5},{1,1,1,5,2},{1,1,2,1,5},{ 1,1,2,5,1},{1,1,2,6,2},{1,1,2,6,6},{1,1,3,1,4},{1,1,3,4,1},{1, 1,4,1,3},{1,1,4,3,1},{1,1,5,1,2},{1,1,5,2,1},{1,1,5,5,6},{1,1, 5,6,5},{1,2,1,1,5},{1,2,1,5,1},{1,2,5,1,1},{1,2,5,1,5},{1,2,6, 2,1},{1,3,1,1,4},{1,3,1,4,1},{1,3,4,1,1},{1,4,1,1,3},{1,4,1,3, 1},{1,4,3,1,1},{1,4,5,1,5},{1,5,1,1,2},{1,5,1,2,1},{1,5,1,5,2} ,{1,5,1,5,4},{1,5,2,1,1},{1,5,2,1,5},{1,5,2,5,1},{1,5,4,1,5},{ 1,5,4,5,1},{1,5,5,1,2},{1,5,5,1,4},{1,5,6,6,6},{2,1,1,1,5},{2, 1,1,5,1},{2,1,5,1,1},{2,1,5,1,5},{2,1,5,5,1},{2,5,1,1,1},{2,5, 1,1,5},{2,5,1,5,1},{2,5,1,5,5},{2,5,5,1,5},{2,6,2,1,1},{3,1,1, 1,4},{3,1,1,4,1},{3,1,4,1,1},{3,4,1,1,1},{4,1,1,1,3},{4,1,1,3,
1},{4,1,3,1,1},{4,1,5,1,5},{4,1,5,5,1},{4,3,1,1,1},{4,5,1,1,5} ,{4,5,1,5,1},{5,1,1,1,2},{5,1,1,2,1},{5,1,1,5,2},{5,1,1,5,4},{ 5,1,2,1,1},{5,1,2,1,5},{5,1,2,5,1},{5,1,4,1,5},{5,1,4,5,1},{5, 1,5,1,2},{5,1,5,1,4},{5,1,5,2,1},{5,1,5,2,5},{5,1,5,4,1},{5,1, 5,5,2},{5,1,5,5,6},{5,1,5,6,5},{5,2,5,1,5},{5,4,1,1,1},{5,5,1, 5,2},{5,5,1,5,6},{5,6,5,1,1},{5,6,5,1,5},{6,5,1,5,5},{6,5,5,1, 1},{6,5,5,1,5},{6,6,2,1,1},{6,6,6,5,1},{1,5,2,6,2},{1,5,2,6,6} ,{1,5,6,2,6},{1,5,6,6,2},{2,6,2,1,5},{2,6,2,5,1},{2,6,6,5,1},{ 5,1,2,6,2},{5,1,2,6,6},{6,2,1,5,6},{6,2,6,5,1},{6,5,1,2,6},{6, 6,2,1,5},{6,6,2,5,1}}
有 6 个匹配数,总共 296 .如下:
{{1,1,1,2,5},{1,1,1,3,6},{1,1,2,2,6},{1,1,2,3,3},{1,1,3,2,3},{ 1,1,3,3,2},{1,1,4,6,6},{1,1,5,2,5},{1,1,5,4,5},{1,1,5,5,2},{1, 1,5,5,4},{1,2,1,2,6},{1,2,1,3,3},{1,2,1,5,5},{1,2,3,1,3},{1,2, 3,3,1},{1,2,3,3,3},{1,2,5,5,1},{1,3,1,2,3},{1,3,1,3,2},{1,3,2, 1,3},{1,3,2,3,1},{1,3,2,3,3},{1,3,3,1,2},{1,3,3,2,1},{1,3,3,2, 3},{1,3,3,3,2},{1,3,6,6,6},{1,4,1,5,5},{1,4,5,5,1},{1,5,1,2,5} ,{1,5,1,4,5},{1,5,2,5,5},{1,5,5,2,1},{1,5,5,2,5},{1,5,5,4,1},{ 1,5,5,5,2},{1,5,5,5,6},{1,5,5,6,5},{1,5,6,5,5},{2,1,1,2,6},{2, 1,1,3,3},{2,1,1,5,5},{2,1,3,1,3},{2,1,3,3,1},{2,1,3,3,3},{2,1, 5,5,5},{2,3,1,1,3},{2,3,1,3,1},{2,3,1,3,3},{2,3,3,1,1},{2,3,3, 1,3},{2,3,3,3,1},{2,5,5,1,1},{2,5,5,5,1},{2,6,2,4,6},{2,6,2,5, 5},{2,6,2,6,4},{2,6,3,3,6},{2,6,3,6,3},{2,6,4,2,6},{2,6,4,6,2} ,{2,6,4,6,6},{2,6,6,2,4},{2,6,6,3,3},{2,6,6,4,6},{2,6,6,6,4},{ 3,1,1,2,3},{3,1,1,3,2},{3,1,2,1,3},{3,1,2,3,1},{3,1,2,3,3},{3, 1,3,1,2},{3,1,3,2,1},{3,1,3,2,3},{3,1,3,3,2},{3,2,1,1,3},{3,2, 1,3,1},{3,2,1,3,3},{3,2,3,1,1},{3,2,3,1,3},{3,2,3,3,1},{3,2,6, 3,6},{3,2,6,6,3},{3,3,1,1,2},{3,3,1,2,1},{3,3,1,2,3},{3,3,1,3, 2},{3,3,2,1,1},{3,3,2,1,3},{3,3,2,3,1},{3,3,2,6,6},{3,3,3,1,2} ,{3,3,3,2,1},{3,3,6,2,6},{3,3,6,6,2},{3,5,6,6,6},{3,6,2,3,6},{ 3,6,2,6,3},{3,6,3,2,6},{3,6,3,6,2},{3,6,5,6,6},{3,6,6,2,3},{3, 6,6,5,6},{3,6,6,6,5},{4,1,1,5,5},{4,2,6,2,6},{4,2,6,6,2},{4,2, 6,6,6},{4,5,1,5,5},{4,5,5,1,1},{4,5,5,1,5},{4,6,2,2,6},{4,6,2, 6,2},{4,6,2,6,6},{4,6,6,2,6},{4,6,6,6,2},{5,1,1,2,5},{5,1,1,4, 5},{5,1,2,5,5},{5,1,5,4,5},{5,1,5,5,4},{5,2,1,1,1},{5,2,1,1,5} ,{5,2,1,5,1},{5,2,1,5,5},{5,2,5,1,1},{5,2,5,5,1},{5,2,6,2,5},{ 5,3,6,6,6},{5,4,1,1,5},{5,4,1,5,1},{5,4,5,1,1},{5,4,5,1,5},{5, 5,1,1,2},{5,5,1,1,4},{5,5,1,2,1},{5,5,1,2,5},{5,5,1,4,1},{5,5, 1,5,4},{5,5,2,1,5},{5,5,2,5,1},{5,5,2,6,2},{5,5,5,1,2},{5,5,6, 5,1},{5,6,3,6,6},{5,6,5,5,1},{5,6,6,3,6},{5,6,6,6,3},{6,2,1,1, 2},{6,2,1,2,1},{6,2,2,1,1},{6,2,2,6,4},{6,2,3,3,6},{6,2,3,6,3} ,{6,2,4,2,6},{6,2,4,6,2},{6,2,4,6,6},{6,2,6,2,4},{6,2,6,3,3},{
3,3,6,2},{6,3,5,6,6},{6,3,6,2,3},{6,3,6,5,6},{6,3,6,6,5},{6,4, 2,6,2},{6,4,2,6,6},{6,4,6,2,6},{6,4,6,6,2},{6,5,3,6,6},{6,5,5, 5,1},{6,5,6,3,6},{6,5,6,6,3},{6,6,2,3,3},{6,6,2,4,6},{6,6,2,6, 4},{6,6,3,5,6},{6,6,3,6,5},{6,6,4,1,1},{6,6,4,2,6},{6,6,4,6,2} ,{6,6,5,3,6},{6,6,5,6,3},{6,6,6,2,4},{6,6,6,3,1},{6,6,6,3,5},{ 6,6,6,5,3},{1,1,2,6,4},{1,1,4,2,6},{1,1,4,6,2},{1,1,5,3,6},{1, 1,5,6,3},{1,2,6,2,3},{1,2,6,2,5},{1,2,6,3,6},{1,2,6,4,1},{1,2, 6,5,6},{1,2,6,6,3},{1,2,6,6,5},{1,3,1,5,6},{1,3,2,6,2},{1,3,2, 6,6},{1,3,6,2,6},{1,3,6,5,1},{1,3,6,6,2},{1,4,1,2,6},{1,4,6,2, 1},{1,5,1,3,6},{1,5,2,2,6},{1,5,4,6,6},{1,5,6,2,2},{1,5,6,3,1} ,{1,5,6,4,6},{1,5,6,6,4},{2,1,5,2,6},{2,1,5,6,2},{2,1,5,6,6},{ 2,2,6,5,1},{2,5,1,2,6},{2,6,2,1,3},{2,6,2,3,1},{2,6,4,1,1},{2, 6,5,1,2},{2,6,6,3,1},{3,1,1,5,6},{3,1,2,6,2},{3,1,2,6,6},{3,2, 6,2,1},{3,5,1,5,6},{3,6,5,1,1},{3,6,5,1,5},{3,6,6,2,1},{4,1,1, 2,6},{4,1,5,6,6},{4,6,2,1,1},{4,6,6,5,1},{5,1,1,3,6},{5,1,2,2, 6},{5,1,4,6,6},{5,1,5,3,6},{5,1,5,6,3},{5,2,6,2,1},{5,6,6,2,1} ,{6,2,1,1,4},{6,2,1,3,6},{6,2,1,4,1},{6,2,1,5,2},{6,2,2,1,5},{ 6,2,2,5,1},{6,2,4,1,1},{6,2,5,1,2},{6,2,6,3,1},{6,3,1,1,5},{6, 3,1,2,6},{6,3,1,5,1},{6,3,5,1,1},{6,3,5,1,5},{6,3,6,2,1},{6,4, 1,5,6},{6,4,6,5,1},{6,5,1,1,3},{6,5,1,3,1},{6,5,1,4,6},{6,5,1, 5,3},{6,5,6,2,1},{6,6,2,1,3},{6,6,2,3,1},{6,6,4,1,5},{6,6,4,5, 1},{6,6,5,1,2},{6,6,5,1,4},{1,5,2,6,4},{1,5,4,2,6},{1,5,4,6,2} ,{1,5,6,2,4},{2,6,4,1,5},{2,6,4,5,1},{2,6,5,1,4},{4,1,5,2,6},{ 4,1,5,6,2},{4,2,6,5,1},{4,5,1,2,6},{4,6,2,1,5},{4,6,2,5,1},{5, 1,2,6,4},{5,1,4,2,6},{5,1,4,6,2},{6,2,1,5,4},{6,2,4,1,5},{6,2, 4,5,1},{6,2,5,1,4}}
有 7 个匹配数,总共 699 .如下:
{{1,1,2,4,4},{1,1,2,5,5},{1,1,3,3,4},{1,1,3,3,6},{1,1,3,4,3},{ 1,1,3,6,3},{1,1,4,2,4},{1,1,4,3,3},{1,1,4,4,2},{1,1,4,4,6},{1, 1,4,5,5},{1,1,4,6,4},{1,2,1,4,4},{1,2,2,2,3},{1,2,2,3,2},{1,2, 3,2,2},{1,2,4,1,4},{1,2,4,4,1},{1,2,5,5,5},{1,3,1,3,4},{1,3,1, 3,6},{1,3,1,4,3},{1,3,2,2,2},{1,3,3,1,4},{1,3,3,4,1},{1,3,4,1, 3},{1,3,4,3,1},{1,3,6,3,1},{1,4,1,2,4},{1,4,1,3,3},{1,4,1,4,2} ,{1,4,1,4,6},{1,4,2,1,4},{1,4,2,4,1},{1,4,3,1,3},{1,4,3,3,1},{ 1,4,4,1,2},{1,4,4,2,1},{1,4,6,4,1},{1,5,2,2,2},{1,5,4,4,4},{1, 5,4,5,5},{1,5,5,4,5},{1,5,5,5,4},{2,1,1,4,4},{2,1,2,2,3},{2,1, 2,3,2},{2,1,3,2,2},{2,1,4,1,4},{2,1,4,4,1},{2,1,5,2,2},{2,2,1, 2,3},{2,2,1,3,2},{2,2,1,5,2},{2,2,2,1,3},{2,2,2,1,5},{2,2,2,3, 1},{2,2,2,5,1},{2,2,3,1,2},{2,2,3,2,1},{2,2,5,1,2},{2,2,6,2,4} ,{2,2,6,4,6},{2,2,6,5,5},{2,2,6,6,4},{2,3,1,2,2},{2,3,2,1,2},{ 2,3,2,2,1},{2,3,3,6,6},{2,3,6,3,6},{2,3,6,6,3},{2,4,1,1,4},{2,
6,6,2},{2,4,6,6,6},{2,5,1,2,2},{2,5,2,6,5},{2,5,5,2,6},{2,5,5, 6,2},{2,5,6,2,5},{2,6,2,2,4},{2,6,2,3,3},{2,6,2,4,2},{2,6,2,4, 4},{2,6,4,4,6},{2,6,4,6,4},{2,6,5,2,5},{2,6,5,5,2},{2,6,5,5,6} ,{2,6,5,6,5},{2,6,6,4,2},{2,6,6,4,4},{2,6,6,5,5},{3,1,1,3,4},{ 3,1,1,3,6},{3,1,1,4,3},{3,1,2,2,2},{3,1,3,1,4},{3,1,3,4,1},{3, 1,4,1,3},{3,1,4,3,1},{3,2,1,2,2},{3,2,2,1,2},{3,2,2,2,1},{3,2, 3,6,6},{3,2,6,2,3},{3,3,1,1,4},{3,3,1,4,1},{3,3,2,6,2},{3,3,3, 4,5},{3,3,3,5,4},{3,3,3,5,6},{3,3,3,6,5},{3,3,4,1,1},{3,3,4,3, 5},{3,3,4,5,3},{3,3,4,6,6},{3,3,5,3,4},{3,3,5,3,6},{3,3,5,4,3} ,{3,3,5,6,3},{3,3,6,3,5},{3,3,6,4,6},{3,3,6,5,3},{3,3,6,6,4},{ 3,4,1,1,3},{3,4,1,3,1},{3,4,3,1,1},{3,4,3,3,5},{3,4,3,5,3},{3, 4,3,6,6},{3,4,5,3,3},{3,4,5,5,5},{3,4,6,3,6},{3,4,6,6,3},{3,5, 3,3,4},{3,5,3,3,6},{3,5,3,4,3},{3,5,3,6,3},{3,5,4,3,3},{3,5,4, 5,5},{3,5,5,4,5},{3,5,5,5,4},{3,5,6,3,3},{3,6,3,1,1},{3,6,3,3, 5},{3,6,3,4,6},{3,6,3,5,3},{3,6,3,6,4},{3,6,4,3,6},{3,6,4,6,3} ,{3,6,5,3,3},{3,6,6,3,2},{3,6,6,3,4},{3,6,6,4,3},{4,1,1,2,4},{ 4,1,1,3,3},{4,1,1,4,2},{4,1,1,4,6},{4,1,2,1,4},{4,1,2,4,1},{4, 1,3,1,3},{4,1,3,3,1},{4,1,4,1,2},{4,1,4,2,1},{4,1,5,4,4},{4,1, 5,5,5},{4,2,1,1,4},{4,2,1,4,1},{4,2,2,6,2},{4,2,2,6,6},{4,2,4, 1,1},{4,2,6,2,2},{4,2,6,2,4},{4,2,6,4,6},{4,2,6,6,4},{4,3,1,1, 3},{4,3,1,3,1},{4,3,3,1,1},{4,3,3,3,5},{4,3,3,5,3},{4,3,3,6,6} ,{4,3,5,3,3},{4,3,5,5,5},{4,3,6,3,6},{4,3,6,6,3},{4,4,1,1,2},{ 4,4,1,2,1},{4,4,1,5,4},{4,4,2,1,1},{4,4,2,6,2},{4,4,2,6,6},{4, 4,4,1,5},{4,4,4,5,1},{4,4,5,1,4},{4,4,6,2,6},{4,4,6,6,2},{4,5, 1,4,4},{4,5,3,3,3},{4,5,3,5,5},{4,5,5,3,5},{4,5,5,5,1},{4,5,5, 5,3},{4,5,5,6,6},{4,5,6,5,6},{4,5,6,6,5},{4,6,2,4,6},{4,6,2,6, 4},{4,6,3,3,6},{4,6,3,6,3},{4,6,4,1,1},{4,6,4,2,6},{4,6,4,6,2} ,{4,6,5,5,6},{4,6,5,6,5},{4,6,6,2,2},{4,6,6,2,4},{4,6,6,3,3},{ 4,6,6,5,5},{5,1,2,2,2},{5,1,4,4,4},{5,1,4,5,5},{5,2,2,6,5},{5, 2,5,2,6},{5,2,5,6,2},{5,2,6,5,2},{5,2,6,5,6},{5,2,6,6,5},{5,3, 3,3,4},{5,3,3,3,6},{5,3,3,4,3},{5,3,3,6,3},{5,3,4,3,3},{5,3,4, 5,5},{5,3,5,4,5},{5,3,5,5,4},{5,3,6,3,3},{5,4,1,5,5},{5,4,3,3, 3},{5,4,3,5,5},{5,4,5,3,5},{5,4,5,5,1},{5,4,5,5,3},{5,4,5,6,6} ,{5,4,6,5,6},{5,4,6,6,5},{5,5,1,4,5},{5,5,2,1,1},{5,5,2,2,6},{ 5,5,2,6,6},{5,5,3,4,5},{5,5,3,5,4},{5,5,4,1,1},{5,5,4,1,5},{5, 5,4,3,5},{5,5,4,5,1},{5,5,4,5,3},{5,5,4,6,6},{5,5,5,1,4},{5,5, 5,2,1},{5,5,5,3,4},{5,5,5,4,3},{5,5,6,2,2},{5,5,6,2,6},{5,5,6, 4,6},{5,5,6,6,2},{5,5,6,6,4},{5,6,2,2,5},{5,6,2,5,2},{5,6,2,5, 6},{5,6,2,6,5},{5,6,3,3,3},{5,6,4,5,6},{5,6,4,6,5},{5,6,5,2,6} ,{5,6,5,4,6},{5,6,5,6,2},{5,6,5,6,4},{5,6,6,2,5},{5,6,6,4,5},{ 5,6,6,5,4},{6,2,2,4,6},{6,2,2,5,5},{6,2,4,4,6},{6,2,4,6,4},{6, 2,5,2,5},{6,2,5,5,2},{6,2,5,5,6},{6,2,5,6,5},{6,2,6,4,2},{6,2, 6,4,4},{6,2,6,5,5},{6,3,1,1,3},{6,3,1,3,1},{6,3,2,3,6},{6,3,3,
6},{6,3,4,6,3},{6,3,5,3,3},{6,3,6,3,2},{6,3,6,3,4},{6,3,6,4,3} ,{6,4,1,1,4},{6,4,1,4,1},{6,4,2,2,6},{6,4,2,6,4},{6,4,3,3,6},{ 6,4,3,6,3},{6,4,4,1,1},{6,4,4,2,6},{6,4,4,6,2},{6,4,5,5,6},{6, 4,5,6,5},{6,4,6,2,2},{6,4,6,2,4},{6,4,6,3,3},{6,4,6,5,5},{6,5, 2,6,5},{6,5,3,3,3},{6,5,4,5,6},{6,5,4,6,5},{6,5,5,2,6},{6,5,5, 4,6},{6,5,5,6,2},{6,5,5,6,4},{6,5,6,2,5},{6,5,6,4,5},{6,5,6,5, 4},{6,6,2,2,4},{6,6,2,4,2},{6,6,2,4,4},{6,6,2,5,5},{6,6,3,2,3} ,{6,6,3,3,2},{6,6,3,3,4},{6,6,3,4,3},{6,6,4,3,3},{6,6,4,5,5},{ 6,6,5,4,5},{6,6,5,5,4},{6,6,6,4,2},{1,1,2,4,6},{1,1,3,5,6},{1, 1,3,6,5},{1,1,5,2,3},{1,1,5,3,2},{1,1,5,3,4},{1,1,5,4,3},{1,2, 1,4,6},{1,2,1,5,3},{1,2,2,6,3},{1,2,2,6,5},{1,2,3,1,5},{1,2,3, 2,6},{1,2,3,5,1},{1,2,3,6,2},{1,2,3,6,6},{1,2,5,1,3},{1,2,5,2, 6},{1,2,5,6,2},{1,2,5,6,6},{1,2,6,3,2},{1,2,6,5,2},{1,3,1,5,2} ,{1,3,1,5,4},{1,3,2,1,5},{1,3,2,2,6},{1,3,2,5,1},{1,3,4,1,5},{ 1,3,4,5,1},{1,3,4,6,6},{1,3,5,1,2},{1,3,5,1,4},{1,3,6,2,2},{1, 3,6,4,6},{1,3,6,6,4},{1,4,1,5,3},{1,4,3,1,5},{1,4,3,5,1},{1,4, 3,6,6},{1,4,5,1,3},{1,4,5,6,6},{1,4,6,3,6},{1,4,6,5,6},{1,4,6, 6,3},{1,4,6,6,5},{1,5,1,2,3},{1,5,1,3,2},{1,5,1,3,4},{1,5,1,4, 3},{1,5,2,1,3},{1,5,2,3,1},{1,5,3,1,2},{1,5,3,1,4},{1,5,3,2,1} ,{1,5,3,3,6},{1,5,3,4,1},{1,5,3,5,6},{1,5,3,6,3},{1,5,3,6,5},{ 1,5,4,1,3},{1,5,4,3,1},{1,5,4,4,6},{1,5,4,6,4},{1,5,5,3,6},{1, 5,5,6,3},{1,5,6,3,3},{1,5,6,3,5},{1,5,6,4,4},{1,5,6,5,3},{2,1, 1,4,6},{2,1,1,5,3},{2,1,2,6,3},{2,1,2,6,5},{2,1,3,1,5},{2,1,3, 2,6},{2,1,3,5,1},{2,1,3,6,2},{2,1,3,6,6},{2,1,5,1,3},{2,1,5,3, 1},{2,2,1,5,6},{2,2,6,3,1},{2,3,1,1,5},{2,3,1,2,6},{2,3,1,5,1} ,{2,3,5,1,1},{2,3,5,1,5},{2,3,6,2,1},{2,5,1,1,3},{2,5,1,3,1},{ 2,5,1,5,3},{2,5,6,2,1},{2,6,2,3,5},{2,6,2,5,3},{2,6,3,1,2},{2, 6,3,2,1},{2,6,3,5,6},{2,6,3,6,5},{2,6,5,2,1},{2,6,5,3,6},{2,6, 5,6,3},{2,6,6,3,5},{2,6,6,5,3},{3,1,1,5,2},{3,1,1,5,4},{3,1,2, 1,5},{3,1,2,2,6},{3,1,2,5,1},{3,1,4,1,5},{3,1,4,5,1},{3,1,4,6, 6},{3,1,5,1,2},{3,1,5,1,4},{3,1,5,2,1},{3,1,5,3,6},{3,1,5,4,1} ,{3,1,5,5,6},{3,1,5,6,3},{3,1,5,6,5},{3,2,1,1,5},{3,2,1,2,6},{ 3,2,1,5,1},{3,2,5,1,1},{3,2,5,1,5},{3,2,6,2,5},{3,2,6,5,6},{3, 2,6,6,5},{3,3,1,5,6},{3,3,6,5,1},{3,4,1,1,5},{3,4,1,5,1},{3,4, 5,1,1},{3,4,5,1,5},{3,5,1,1,2},{3,5,1,1,4},{3,5,1,2,1},{3,5,1, 3,6},{3,5,1,4,1},{3,5,1,5,2},{3,5,1,5,4},{3,5,2,6,2},{3,5,2,6, 6},{3,5,6,2,6},{3,5,6,5,1},{3,5,6,6,2},{3,6,2,1,2},{3,6,2,2,1} ,{3,6,2,5,6},{3,6,2,6,5},{3,6,3,1,5},{3,6,3,5,1},{3,6,5,1,3},{ 3,6,5,2,6},{3,6,5,5,1},{3,6,5,6,2},{3,6,6,2,5},{3,6,6,4,1},{4, 1,1,5,3},{4,1,3,1,5},{4,1,3,5,1},{4,1,3,6,6},{4,1,5,1,3},{4,1, 5,3,1},{4,1,5,4,6},{4,1,5,6,4},{4,3,1,1,5},{4,3,1,5,1},{4,3,5, 1,1},{4,3,5,1,5},{4,4,1,5,6},{4,4,6,5,1},{4,5,1,1,3},{4,5,1,3, 1},{4,5,1,4,6},{4,5,1,5,3},{4,6,4,1,5},{4,6,4,5,1},{4,6,5,1,4}
5,1,2,1,3},{5,1,2,3,1},{5,1,3,1,2},{5,1,3,1,4},{5,1,3,2,1},{5, 1,3,3,6},{5,1,3,4,1},{5,1,3,5,6},{5,1,3,6,3},{5,1,3,6,5},{5,1, 4,1,3},{5,1,4,3,1},{5,1,4,4,6},{5,1,4,6,4},{5,1,5,2,3},{5,1,5, 3,2},{5,1,5,3,4},{5,1,5,4,3},{5,2,1,2,6},{5,2,6,2,3},{5,2,6,3, 6},{5,2,6,6,3},{5,3,1,5,6},{5,3,2,6,2},{5,3,2,6,6},{5,3,6,2,6} ,{5,3,6,5,1},{5,3,6,6,2},{5,5,1,3,6},{5,6,2,1,2},{5,6,2,2,1},{ 5,6,2,3,6},{5,6,2,6,3},{5,6,3,1,1},{5,6,3,1,5},{5,6,3,2,6},{5, 6,3,5,1},{5,6,3,6,2},{5,6,5,1,3},{5,6,6,2,3},{5,6,6,4,1},{6,2, 1,2,3},{6,2,1,2,5},{6,2,1,3,2},{6,2,2,1,3},{6,2,2,3,1},{6,2,3, 1,2},{6,2,3,2,1},{6,2,3,5,6},{6,2,3,6,5},{6,2,5,2,1},{6,2,5,3, 6},{6,2,5,6,3},{6,2,6,3,5},{6,2,6,5,3},{6,3,1,4,6},{6,3,1,5,3} ,{6,3,1,5,5},{6,3,2,6,5},{6,3,3,1,5},{6,3,3,5,1},{6,3,5,1,3},{ 6,3,5,2,6},{6,3,5,5,1},{6,3,5,6,2},{6,3,6,2,5},{6,3,6,4,1},{6, 4,1,1,2},{6,4,1,2,1},{6,4,1,3,6},{6,4,1,5,4},{6,4,2,1,1},{6,4, 4,1,5},{6,4,4,5,1},{6,4,5,1,4},{6,4,6,3,1},{6,5,1,2,2},{6,5,1, 3,3},{6,5,1,3,5},{6,5,1,4,4},{6,5,2,6,3},{6,5,3,1,1},{6,5,3,1, 5},{6,5,3,2,6},{6,5,3,5,1},{6,5,3,6,2},{6,5,5,1,3},{6,5,6,2,3} ,{6,5,6,4,1},{6,6,2,3,5},{6,6,2,5,3},{6,6,3,1,2},{6,6,3,1,4},{ 6,6,3,2,1},{6,6,3,4,1},{6,6,4,1,3},{6,6,4,3,1},{6,6,5,2,1},{6, 6,5,4,1},{1,2,6,3,4},{1,2,6,4,3},{1,2,6,4,5},{1,2,6,5,4},{1,3, 2,6,4},{1,3,4,2,6},{1,3,4,6,2},{1,3,6,2,4},{1,4,2,6,3},{1,4,2, 6,5},{1,4,3,2,6},{1,4,3,6,2},{1,4,5,2,6},{1,4,5,6,2},{1,4,6,2, 3},{1,4,6,2,5},{1,5,2,4,6},{1,5,6,4,2},{2,1,5,4,6},{2,1,5,6,4} ,{2,4,1,5,6},{2,4,6,5,1},{2,5,1,4,6},{2,6,3,1,4},{2,6,3,4,1},{ 2,6,4,1,3},{2,6,4,3,1},{2,6,5,4,1},{3,1,2,6,4},{3,1,4,2,6},{3, 1,4,6,2},{3,2,6,4,1},{3,4,1,2,6},{3,4,6,2,1},{3,6,2,1,4},{3,6, 2,4,1},{4,1,2,6,3},{4,1,2,6,5},{4,1,3,2,6},{4,1,3,6,2},{4,2,1, 5,6},{4,2,6,3,1},{4,3,1,2,6},{4,3,6,2,1},{4,5,6,2,1},{4,6,2,1, 3},{4,6,2,3,1},{4,6,5,1,2},{5,1,2,4,6},{5,2,6,4,1},{5,4,1,2,6} ,{5,4,6,2,1},{5,6,2,1,4},{5,6,2,4,1},{6,2,1,3,4},{6,2,1,4,3},{ 6,2,1,4,5},{6,2,3,1,4},{6,2,3,4,1},{6,2,4,1,3},{6,2,4,3,1},{6, 2,5,4,1},{6,4,1,5,2},{6,4,2,1,5},{6,4,2,5,1},{6,4,5,1,2},{6,5, 1,2,4},{6,5,1,4,2}}
有 8 个匹配数,总共 901 .如下:
{{1,1,2,2,4},{1,1,2,4,2},{1,1,4,2,2},{1,2,1,2,4},{1,2,1,4,2},{ 1,2,2,1,4},{1,2,2,2,5},{1,2,2,4,1},{1,2,2,5,2},{1,2,4,1,2},{1, 2,4,2,1},{1,2,5,2,2},{1,3,3,3,4},{1,3,3,3,6},{1,3,3,4,3},{1,3, 3,6,3},{1,3,4,3,3},{1,3,4,4,4},{1,3,6,3,3},{1,4,1,2,2},{1,4,2, 1,2},{1,4,2,2,1},{1,4,3,3,3},{1,4,3,4,4},{1,4,4,3,4},{1,4,4,4, 3},{1,4,4,4,5},{1,4,4,5,4},{1,4,5,4,4},{1,4,5,5,5},{2,1,1,2,4} ,{2,1,1,4,2},{2,1,2,1,4},{2,1,2,2,5},{2,1,2,4,1},{2,1,2,5,2},{
2,2,6,4},{2,2,4,1,1},{2,2,4,2,6},{2,2,4,6,2},{2,2,4,6,6},{2,2, 5,2,1},{2,2,5,5,6},{2,2,5,6,5},{2,2,6,3,3},{2,2,6,4,2},{2,2,6, 4,4},{2,3,2,6,3},{2,3,3,2,6},{2,3,3,6,2},{2,3,5,5,5},{2,3,6,2, 3},{2,4,1,1,2},{2,4,1,2,1},{2,4,2,1,1},{2,4,2,2,6},{2,4,2,6,4} ,{2,4,4,2,6},{2,4,4,6,2},{2,4,4,6,6},{2,4,6,2,2},{2,4,6,2,4},{ 2,4,6,4,6},{2,4,6,6,4},{2,5,2,1,2},{2,5,2,2,1},{2,5,2,5,6},{2, 5,3,5,5},{2,5,5,3,5},{2,5,5,5,3},{2,5,5,6,6},{2,5,6,5,2},{2,5, 6,5,6},{2,5,6,6,5},{2,6,3,2,3},{2,6,3,3,2},{2,6,4,2,2},{2,6,4, 2,4},{2,6,4,4,2},{2,6,4,4,4},{3,1,3,3,4},{3,1,3,3,6},{3,1,3,4, 3},{3,1,3,6,3},{3,1,4,3,3},{3,1,4,4,4},{3,2,2,6,3},{3,2,3,2,6} ,{3,2,3,6,2},{3,2,5,5,5},{3,2,6,3,2},{3,3,1,3,4},{3,3,1,3,6},{ 3,3,1,4,3},{3,3,2,2,6},{3,3,3,1,4},{3,3,3,4,1},{3,3,4,1,3},{3, 3,4,3,1},{3,3,4,5,5},{3,3,5,4,5},{3,3,5,5,4},{3,3,5,5,6},{3,3, 5,6,5},{3,3,6,2,2},{3,3,6,3,1},{3,3,6,5,5},{3,4,1,3,3},{3,4,1, 4,4},{3,4,3,1,3},{3,4,3,3,1},{3,4,3,5,5},{3,4,4,1,4},{3,4,4,4, 1},{3,4,4,4,5},{3,4,4,5,4},{3,4,5,3,5},{3,4,5,4,4},{3,4,5,5,3} ,{3,5,2,5,5},{3,5,3,4,5},{3,5,3,5,4},{3,5,3,5,6},{3,5,3,6,5},{ 3,5,4,3,5},{3,5,4,4,4},{3,5,4,5,3},{3,5,5,2,5},{3,5,5,3,4},{3, 5,5,3,6},{3,5,5,4,3},{3,5,5,5,2},{3,5,5,5,6},{3,5,5,6,3},{3,5, 5,6,5},{3,5,6,3,5},{3,5,6,5,3},{3,5,6,5,5},{3,6,2,2,3},{3,6,2, 3,2},{3,6,3,1,3},{3,6,3,3,1},{3,6,3,5,5},{3,6,5,3,5},{3,6,5,5, 3},{3,6,5,5,5},{4,1,1,2,2},{4,1,2,1,2},{4,1,2,2,1},{4,1,3,3,3} ,{4,1,3,4,4},{4,1,4,3,4},{4,1,4,4,3},{4,1,4,4,5},{4,1,4,5,4},{ 4,2,1,1,2},{4,2,1,2,1},{4,2,2,1,1},{4,2,2,2,6},{4,2,2,6,4},{4, 2,4,2,6},{4,2,4,6,2},{4,2,4,6,6},{4,2,6,4,2},{4,2,6,4,4},{4,3, 1,3,3},{4,3,1,4,4},{4,3,3,1,3},{4,3,3,3,1},{4,3,3,5,5},{4,3,4, 1,4},{4,3,4,4,1},{4,3,4,4,5},{4,3,4,5,4},{4,3,5,3,5},{4,3,5,4, 4},{4,3,5,5,3},{4,4,1,3,4},{4,4,1,4,3},{4,4,1,4,5},{4,4,2,2,6} ,{4,4,2,6,4},{4,4,3,1,4},{4,4,3,4,1},{4,4,3,4,5},{4,4,3,5,4},{ 4,4,4,1,3},{4,4,4,2,6},{4,4,4,3,1},{4,4,4,3,5},{4,4,4,5,3},{4, 4,4,6,2},{4,4,5,3,4},{4,4,5,4,1},{4,4,5,4,3},{4,4,5,5,6},{4,4, 5,6,5},{4,4,6,2,2},{4,4,6,2,4},{4,4,6,5,5},{4,5,3,3,5},{4,5,3, 4,4},{4,5,3,5,3},{4,5,4,1,4},{4,5,4,3,4},{4,5,4,4,1},{4,5,4,4, 3},{4,5,4,5,6},{4,5,4,6,5},{4,5,5,3,3},{4,5,5,4,6},{4,5,5,6,4} ,{4,5,6,4,5},{4,5,6,5,4},{4,6,2,2,2},{4,6,2,2,4},{4,6,2,4,2},{ 4,6,2,4,4},{4,6,4,5,5},{4,6,5,4,5},{4,6,5,5,4},{4,6,6,4,2},{5, 2,1,2,2},{5,2,2,1,2},{5,2,2,2,1},{5,2,2,5,6},{5,2,3,5,5},{5,2, 5,3,5},{5,2,5,5,3},{5,2,5,6,6},{5,3,2,5,5},{5,3,3,4,5},{5,3,3, 5,4},{5,3,3,5,6},{5,3,3,6,5},{5,3,4,3,5},{5,3,4,4,4},{5,3,4,5, 3},{5,3,5,2,5},{5,3,5,3,4},{5,3,5,3,6},{5,3,5,4,3},{5,3,5,5,2} ,{5,3,5,5,6},{5,3,5,6,3},{5,3,5,6,5},{5,3,6,3,5},{5,3,6,5,3},{ 5,3,6,5,5},{5,4,1,4,4},{5,4,3,3,5},{5,4,3,4,4},{5,4,3,5,3},{5, 4,4,1,4},{5,4,4,3,4},{5,4,4,4,1},{5,4,4,4,3},{5,4,4,5,6},{5,4,
5,4},{5,5,2,3,5},{5,5,2,5,3},{5,5,3,2,5},{5,5,3,3,4},{5,5,3,3, 6},{5,5,3,4,3},{5,5,3,5,2},{5,5,3,5,6},{5,5,3,6,3},{5,5,3,6,5} ,{5,5,4,3,3},{5,5,4,4,6},{5,5,4,6,4},{5,5,5,2,3},{5,5,5,3,2},{ 5,5,5,3,6},{5,5,5,4,1},{5,5,5,6,3},{5,5,6,3,3},{5,5,6,3,5},{5, 5,6,4,4},{5,5,6,5,3},{5,6,3,3,5},{5,6,3,5,3},{5,6,3,5,5},{5,6, 4,4,5},{5,6,4,5,4},{5,6,5,2,2},{5,6,5,3,3},{5,6,5,3,5},{5,6,5, 4,4},{5,6,5,5,3},{5,6,6,5,2},{6,2,2,2,4},{6,2,2,3,3},{6,2,2,4, 2},{6,2,2,4,4},{6,2,3,2,3},{6,2,3,3,2},{6,2,4,2,2},{6,2,4,2,4} ,{6,2,4,4,2},{6,2,4,4,4},{6,3,1,3,3},{6,3,3,1,3},{6,3,3,3,1},{ 6,3,3,5,5},{6,3,5,3,5},{6,3,5,5,3},{6,3,5,5,5},{6,4,2,4,6},{6, 4,4,5,5},{6,4,5,4,5},{6,4,5,5,4},{6,4,6,4,2},{6,5,2,2,5},{6,5, 2,5,2},{6,5,2,5,6},{6,5,3,3,5},{6,5,3,5,3},{6,5,3,5,5},{6,5,4, 4,5},{6,5,4,5,4},{6,5,5,2,2},{6,5,5,3,3},{6,5,5,3,5},{6,5,5,4, 4},{6,5,5,5,3},{6,5,6,5,2},{6,6,4,2,2},{6,6,4,2,4},{6,6,4,4,2} ,{6,6,5,2,5},{6,6,5,5,2},{1,1,2,3,5},{1,1,2,5,3},{1,1,3,2,5},{ 1,1,3,4,5},{1,1,3,5,2},{1,1,3,5,4},{1,1,4,3,5},{1,1,4,5,3},{1, 2,1,3,5},{1,2,2,3,6},{1,2,2,5,6},{1,2,5,3,1},{1,3,1,2,5},{1,3, 1,4,5},{1,3,3,5,6},{1,3,3,6,5},{1,3,4,4,6},{1,3,4,6,4},{1,3,5, 2,1},{1,3,5,3,6},{1,3,5,4,1},{1,3,5,5,6},{1,3,5,6,3},{1,3,5,6, 5},{1,3,6,3,5},{1,3,6,4,4},{1,3,6,5,3},{1,3,6,5,5},{1,4,1,3,5} ,{1,4,3,4,6},{1,4,3,6,4},{1,4,4,3,6},{1,4,4,5,6},{1,4,4,6,3},{ 1,4,4,6,5},{1,4,5,3,1},{1,4,5,4,6},{1,4,5,6,4},{1,4,6,3,4},{1, 4,6,4,3},{1,4,6,4,5},{1,4,6,5,4},{1,5,2,2,4},{1,5,2,3,3},{1,5, 2,3,5},{1,5,2,4,2},{1,5,2,4,4},{1,5,2,5,3},{1,5,3,2,3},{1,5,3, 2,5},{1,5,3,3,2},{1,5,3,3,4},{1,5,3,4,3},{1,5,3,4,5},{1,5,3,5, 2},{1,5,3,5,4},{1,5,4,2,2},{1,5,4,2,4},{1,5,4,3,3},{1,5,4,3,5} ,{1,5,4,4,2},{1,5,4,5,3},{1,5,5,2,3},{1,5,5,3,2},{1,5,5,3,4},{ 1,5,5,4,3},{2,1,1,3,5},{2,1,2,3,6},{2,1,2,5,6},{2,1,5,2,4},{2, 1,5,3,3},{2,1,5,3,5},{2,1,5,4,2},{2,1,5,4,4},{2,1,5,5,3},{2,2, 1,3,6},{2,2,1,5,4},{2,2,4,1,5},{2,2,4,5,1},{2,2,5,1,4},{2,2,6, 3,5},{2,2,6,5,3},{2,3,1,5,3},{2,3,1,5,5},{2,3,2,6,5},{2,3,3,1, 5},{2,3,3,5,1},{2,3,5,1,3},{2,3,5,2,6},{2,3,5,5,1},{2,3,5,6,2} ,{2,3,5,6,6},{2,3,6,2,5},{2,3,6,5,6},{2,3,6,6,5},{2,4,1,5,2},{ 2,4,1,5,4},{2,4,2,1,5},{2,4,2,5,1},{2,4,4,1,5},{2,4,4,5,1},{2, 4,5,1,2},{2,4,5,1,4},{2,5,1,2,4},{2,5,1,3,3},{2,5,1,3,5},{2,5, 1,4,2},{2,5,1,4,4},{2,5,2,6,3},{2,5,3,1,1},{2,5,3,1,5},{2,5,3, 2,6},{2,5,3,5,1},{2,5,3,6,2},{2,5,3,6,6},{2,5,5,1,3},{2,5,6,2, 3},{2,5,6,3,6},{2,5,6,6,3},{2,6,3,2,5},{2,6,3,3,4},{2,6,3,4,3} ,{2,6,3,5,2},{2,6,4,3,3},{2,6,4,5,5},{2,6,5,2,3},{2,6,5,3,2},{ 2,6,5,4,5},{2,6,5,5,4},{3,1,1,2,5},{3,1,1,4,5},{3,1,3,5,6},{3, 1,3,6,5},{3,1,4,4,6},{3,1,4,6,4},{3,1,5,2,3},{3,1,5,2,5},{3,1, 5,3,2},{3,1,5,3,4},{3,1,5,4,3},{3,1,5,4,5},{3,1,5,5,2},{3,1,5, 5,4},{3,2,1,5,3},{3,2,1,5,5},{3,2,2,6,5},{3,2,3,1,5},{3,2,3,5,。