鎖具裝箱問(wèn)題的數(shù)學(xué)模型

1、鎖具裝箱問(wèn)題的數(shù)學(xué)模型詹國(guó)武1 黃景文1 周輝莉2（1.05級(jí)化工系； 2.05級(jí)經(jīng)濟(jì)系）摘要：本文針對(duì)鎖具如何裝箱問(wèn)題，建立了一個(gè)新模型，并對(duì)其進(jìn)行了分析和評(píng)價(jià)。就如何裝箱問(wèn)題，本文建立了一個(gè)如何對(duì)每一批鎖具進(jìn)行裝箱和標(biāo)記才能是消費(fèi)者的滿意度最高的模型，再具體分析實(shí)際銷(xiāo)售情況，建立了在消費(fèi)量不同情況下，如何組合已裝箱好的鎖具才能使?jié)M意度最大的模型以及，再對(duì)此模型進(jìn)一步探討和分析，得到一個(gè)當(dāng)銷(xiāo)售箱數(shù)超過(guò)49箱僅僅用同奇或者同偶類(lèi)的鎖具來(lái)組合的模型,并且對(duì)其進(jìn)行了論證,最終得到最優(yōu)的結(jié)果利用軟件通過(guò)篩法，分別求得一批鎖具鑰匙的槽高由3個(gè)，4個(gè)，5個(gè)不同數(shù)組成的個(gè)數(shù)為2544，2808，528，一

2、批鎖具的個(gè)數(shù)和箱數(shù)5880和98。再根據(jù)能夠互開(kāi)的鎖具的條件，且根據(jù)槽高為連續(xù)的整數(shù)特性，得到結(jié)論：當(dāng)一個(gè)鑰匙的槽高之和為奇（偶）時(shí)，他的互開(kāi)鑰匙的槽高和必為偶（奇），即槽高和同為奇（偶）的必不能互開(kāi)，得到把奇偶分開(kāi)裝箱和標(biāo)記的一個(gè)初步方案，為了定量的分析不同的方案，利用概率論的方法，引入了平均互開(kāi)對(duì)的概念。對(duì)于隨后的銷(xiāo)售方案，我們利用圖論知識(shí)，從最小匹配數(shù)入手，通過(guò)對(duì)平均互開(kāi)對(duì)數(shù)的大小比較來(lái)衡量各個(gè)方案和組合的最優(yōu)情況，得到如下結(jié)論，當(dāng)銷(xiāo)售不超過(guò)49箱時(shí)，只銷(xiāo)售槽高和為奇（偶）的，當(dāng)超過(guò)49箱時(shí)則按下問(wèn)所論述的搭配方案，再進(jìn)一步打破陳規(guī)，當(dāng)按下文的裝箱和標(biāo)記，僅僅銷(xiāo)售奇（偶），能夠使抱怨的程

3、度更小。關(guān)鍵詞：篩法 奇偶分箱 同奇或同偶銷(xiāo)售 平均對(duì)開(kāi)數(shù) 顧客抱怨度 最小匹配一問(wèn)題的重述某廠生產(chǎn)一種彈子鎖具，每個(gè)鎖具的鑰匙有5個(gè)槽，每個(gè)槽的高度從1，2，3，4，5，66個(gè)數(shù)中任意的取一數(shù)，但對(duì)于每個(gè)鑰匙的5個(gè)槽高的取值需要滿足以下兩個(gè)條件1至少有3個(gè)不同的數(shù)2相鄰的兩槽的高度差不能為5滿足以上兩個(gè)條件的所有不同的鎖具稱(chēng)為一批，銷(xiāo)售部門(mén)隨意的取60個(gè)裝一箱出售同一批鎖可以互開(kāi)的條件：1. 二者相對(duì)應(yīng)的5個(gè)槽的高度中有4個(gè)相同2. 另一個(gè)槽的高度相差為1由于銷(xiāo)售部門(mén)隨意的取60個(gè)裝一箱，所以同一消費(fèi)者可能買(mǎi)到互開(kāi)的鎖具，導(dǎo)致了消費(fèi)者的不滿。我們的問(wèn)題如下：1每一批鎖具有多少個(gè)，能裝多少箱？

4、2求下面三個(gè)事件的概率：（1）槽的高度由5個(gè)不同數(shù)字組成；（2）槽的高度由4個(gè)不同數(shù)字組成；（3）槽的高度由3個(gè)不同數(shù)字組成。3.銷(xiāo)售部門(mén)如何制定一個(gè)方案，包括如何裝箱（仍舊是60個(gè)鎖具裝一箱），如何給箱子以標(biāo)記，出售時(shí)如何利用這些標(biāo)志，是團(tuán)體顧客不再抱怨或者減少抱怨。二問(wèn)題的分析本題目是要求求出一批鎖具的個(gè)數(shù)和裝箱數(shù)，以及槽的高度由5個(gè)，4個(gè)，3個(gè)不同數(shù)字組成的概率，由于這個(gè)問(wèn)題的數(shù)據(jù)量比較小，對(duì)于這個(gè)可以用mathematic和matlab處理軟件利用篩法，直接求出，。 我們從奇偶性出發(fā)，利用奇偶分類(lèi)的思想和圖論的最小匹配知識(shí)，尋找各個(gè)鎖具的最小匹配數(shù)，發(fā)現(xiàn)在大于49箱時(shí)，奇類(lèi)和偶類(lèi)的匹配

5、數(shù)都一樣，從這里入手，我們建立了自己的模型。 同時(shí)，團(tuán)體購(gòu)買(mǎi)的消費(fèi)者對(duì)產(chǎn)品的抱怨來(lái)自于鎖之間的互開(kāi)程度。于是，我們引入互開(kāi)數(shù)的概念，通過(guò)互開(kāi)率來(lái)進(jìn)行對(duì)費(fèi)者抱怨度的分析，來(lái)評(píng)價(jià)每個(gè)模型。三模型假設(shè)1可以生產(chǎn)槽高精確的鎖具2生產(chǎn)過(guò)程中可以對(duì)每個(gè)槽高進(jìn)行控制，即按所安排的不同鎖具排列順序生產(chǎn)并且可以更改設(shè)置3能夠以上鎖具互開(kāi)條件的一定能夠互開(kāi)4.互開(kāi)對(duì)的百分比與顧客不不滿意度成正比,在這里不妨設(shè)其相等四符號(hào)及概念的說(shuō)明:一批鎖具中槽的高度由5個(gè)不同的數(shù)字組成的鎖具個(gè)數(shù).:一批鎖具中槽的高度由4個(gè)不同的數(shù)組成的鎖具個(gè)數(shù):一批鎖具中槽的高度由3個(gè)不同的數(shù)組成的鎖具個(gè)數(shù)n：一批鎖具的總個(gè)數(shù)m：一批鎖具的箱

6、數(shù)p5：/np4：/np3：/n:第i個(gè)槽的高度h:5個(gè)槽高的和no：一批鎖具中h為奇數(shù)的個(gè)數(shù)ne:一批鎖具中h為偶數(shù)的個(gè)數(shù):一批鎖具中h為奇數(shù)的裝箱數(shù):一批鎖具中h為偶數(shù)的裝箱數(shù)互開(kāi)對(duì):能夠互開(kāi)的鎖具的對(duì)數(shù)五模型的建立與求解1對(duì)本題題目中問(wèn)題的求解 利用mathematic和matlab求得：總數(shù)：n=5880m=98=528=2808=2544從而求得：p5=528÷5880=89.8p4=2808÷5880=477.6p3=2544÷5880=432.62裝箱方案（1）對(duì)問(wèn)題進(jìn)行具體的分析，找到途徑 對(duì)于本題目所給的數(shù)據(jù)進(jìn)行分析，槽的高度選擇為一連續(xù)整數(shù)列，

7、想到某個(gè)鑰匙的h 為一奇數(shù)（偶數(shù)）時(shí)，則其互開(kāi)鑰匙的h必為大1或小1的偶數(shù)（奇數(shù)），這樣我們把h為奇數(shù)的分成一個(gè)集合o,h為偶數(shù)的分為一個(gè)集合e，這樣，同屬于o（e）的之間則一定不能互開(kāi)，當(dāng)在奇數(shù)集o中任意加入一個(gè)h為偶數(shù)的keyl形成新的集合,因?yàn)閗eyl 在o中一定有與其互開(kāi)的鎖，所以元素之間不再為必不互開(kāi)了，所以奇數(shù)集合o（或偶數(shù)集合e）即為任意兩個(gè)元素之間必不互開(kāi)的最大集合。這里通過(guò)把鎖局具進(jìn)行分類(lèi)成為o和e，然后分開(kāi)裝箱和分開(kāi)銷(xiāo)售，就可以盡量的避免互開(kāi)的現(xiàn)象。（2）對(duì)h為奇數(shù)和偶數(shù)的鎖具個(gè)數(shù)的求解設(shè)為任一符合規(guī)格的鎖具的槽高排列令 :在o中鎖具s=,與它互補(bǔ)的一鎖具為因?yàn)?

8、=35 且假設(shè):為奇數(shù)所以: 為偶數(shù)又因?yàn)?且所以有:且得出任一o中所對(duì)應(yīng)的互補(bǔ)鎖具都符合要求:所以有: no ne同理可得: ne no最終得到結(jié)果: ne= no=5880/2=2940(此結(jié)論也同時(shí)用mathematic和matlab 進(jìn)行了驗(yàn)證)所以:=98/2=49（3）.裝箱和標(biāo)記 為了將h為奇數(shù)的和h為偶數(shù)的區(qū)分開(kāi),應(yīng)用不同的標(biāo)記來(lái)表示箱子如標(biāo)上“奇”，“偶”不同字樣,為了讓區(qū)別更叫明顯也可以對(duì)裝不同奇偶性鎖具的箱子用不同的顏色制成,為了使單個(gè)鎖也能區(qū)分其奇偶性,可以把標(biāo)記做在鎖具上,這樣即使箱子損壞或沒(méi)有箱子時(shí)也能區(qū)分其奇偶性,當(dāng)銷(xiāo)售不超過(guò)49箱時(shí),只銷(xiāo)售或中的鎖具則可實(shí)現(xiàn)鎖具

9、不能互開(kāi)的要求,但這里要求出售的是同一批的產(chǎn)品,當(dāng)鎖具有囤積的時(shí)候就難以區(qū)分是否是同一批,所以每一批也應(yīng)該明顯的標(biāo)志出生產(chǎn)批號(hào).3. 對(duì)以上模型的優(yōu)化由于在實(shí)際銷(xiāo)售過(guò)程中往往可能大于49箱,當(dāng)超過(guò)49箱后我們應(yīng)該怎樣組合才能使互開(kāi)的幾率更小呢對(duì)同一批所生產(chǎn)的鎖具進(jìn)行兩兩對(duì)比,看是否能夠互開(kāi),得到能夠互開(kāi)的對(duì)數(shù).此目的可以用mathematica和matlab來(lái)實(shí)現(xiàn),得到的結(jié)果為:u=22778(對(duì))則平均每個(gè)鎖具能組成的互開(kāi)的對(duì)數(shù):=22778/(5880/2)=7.75(對(duì))a.對(duì)于隨機(jī)裝箱的分析在一箱中,對(duì)于任一鎖具s,與其成互開(kāi)對(duì)的平均個(gè)數(shù)為: =0.078(個(gè)) 整箱所對(duì)應(yīng)的互開(kāi)對(duì)為:

10、 =2.33(對(duì)) 利用上面的模型推廣到更為普遍的k箱則有: = =上面的公式對(duì)k都適用b.對(duì)奇偶分開(kāi)裝箱的分析當(dāng)購(gòu)買(mǎi)量不超過(guò)49箱時(shí),不會(huì)出現(xiàn)互開(kāi)的情況,這時(shí)()=0.當(dāng)購(gòu)買(mǎi)超過(guò)49箱時(shí),則先從奇(偶)類(lèi)中抽出49箱,再?gòu)呐?奇)類(lèi)中抽出k-49箱,在前面的49箱和后面的k-49箱的鎖之間才能構(gòu)成互開(kāi)關(guān)系,所以有k箱鎖具中的平均互開(kāi)對(duì)數(shù)為: =7.75×60×( k-49)=465k-22785得到在互開(kāi)次數(shù)的分段函數(shù): c.對(duì)此模型的改進(jìn): 由于不同的鎖具其互開(kāi)對(duì)數(shù)時(shí)不一樣的,（比如對(duì)于每個(gè)偶類(lèi)的鎖，他們能在奇類(lèi)的鎖中找到的互開(kāi)的鎖的數(shù)量是不相同的），我們當(dāng)然希望能夠?qū)?/p>

11、偶（奇）類(lèi)的鎖具按照它們能夠在奇（偶）類(lèi)的鎖中找到互開(kāi)的鎖的多少進(jìn)行分類(lèi),在賣(mài)完一類(lèi)49箱后，先將另一類(lèi)中有互開(kāi)次數(shù)少的先賣(mài)，在賣(mài)有互開(kāi)次數(shù)多的鎖，所以得到方案。這里用mathmatic處理得到各個(gè)鎖具互開(kāi)對(duì)數(shù)以下結(jié)果有4個(gè)互開(kāi)對(duì)數(shù)的共有45個(gè),其分別是: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,

12、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個(gè)互開(kāi)對(duì)數(shù)的共有105個(gè),其分別為:1,1

13、,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

14、,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

15、,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

16、,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個(gè)互開(kāi)對(duì)數(shù)的有296個(gè)(在這里就不詳盡列出來(lái),可考察附錄)；有7個(gè)互開(kāi)對(duì)數(shù)的有699個(gè)(在這里就不詳盡列出來(lái),可考察附錄)；有8個(gè)互開(kāi)對(duì)數(shù)的有901個(gè)(在這里就不詳盡列出來(lái),可考察附錄)；有9個(gè)互開(kāi)對(duì)數(shù)的有744個(gè)(在這里就不詳盡列出來(lái),可考察附錄)；有10個(gè)互開(kāi)對(duì)數(shù)的有105個(gè)(在這里就不詳盡列出來(lái),

17、可考察附錄)；從這里可以看出,我們可以任意選擇奇(偶)作為前面的49箱(本題選擇了奇),對(duì)此奇(偶)類(lèi)的生產(chǎn)可以不必加以排序,隨即生產(chǎn)即可,但若要能夠使后面的匹配得以實(shí)現(xiàn),則不僅僅要區(qū)別出奇偶性,還要區(qū)別產(chǎn)品的生產(chǎn)順序號(hào),在這里之所以列出每個(gè)鎖具對(duì)應(yīng)的槽高數(shù)列,是為了方便安排生產(chǎn),使生產(chǎn)按照互開(kāi)對(duì)數(shù)增加的序列方向進(jìn)行，然后從有互開(kāi)次數(shù)少的鎖開(kāi)始裝箱，比如將45個(gè)有4個(gè)互開(kāi)次數(shù)的鎖和15個(gè)有5個(gè)互開(kāi)次數(shù)的鎖裝一箱，要把有5個(gè)互開(kāi)次數(shù)的鎖放箱子底邊，表示有4個(gè)互開(kāi)次數(shù)的鎖先賣(mài)，依此類(lèi)推。如果生產(chǎn)過(guò)程服從上面所得的數(shù)據(jù)的排列順序則可以很明確的知道何時(shí)生產(chǎn)何等級(jí)的鎖具,然后對(duì)不同等級(jí)的鎖具箱子或直接鎖

18、具上做好明確的標(biāo)記,使搭配可以順利準(zhǔn)確的進(jìn)行所以得到這種方法的互開(kāi)次數(shù)，如下的分段函數(shù):d.消費(fèi)量超過(guò)49箱時(shí),多出的用同奇偶性的鎖具補(bǔ)充的模型由于同為奇(偶)類(lèi)的鎖具,它們能夠互開(kāi)的條件是：必須是相同的鎖當(dāng)k<=49時(shí), =0當(dāng)49<k<=98時(shí),由于在原有的49箱中,每個(gè)奇(偶)的模型都有了,所以每增加一個(gè)鎖具,則其互開(kāi)對(duì)數(shù)增加一個(gè),得到=60(k-49)聯(lián)合上面的,得到: 為了更直觀的比較四種方案,用mathematic畫(huà)出了以上四種模型互開(kāi)次數(shù)與箱數(shù)函數(shù)其中：f1為隨機(jī)裝箱的互開(kāi)對(duì)數(shù)與箱數(shù)函數(shù)； f2為奇偶分開(kāi)裝箱互開(kāi)對(duì)數(shù)與箱數(shù)函數(shù)； f3為奇偶分開(kāi)裝箱又按具有互開(kāi)對(duì)

19、數(shù)多少分類(lèi)的互開(kāi)對(duì)數(shù)與箱數(shù)函數(shù)； f4為都賣(mài)同一類(lèi)鎖（奇或偶）互開(kāi)對(duì)數(shù)與箱數(shù)函數(shù)。 由上可以看出用第四中方案所產(chǎn)生的互開(kāi)對(duì)數(shù)會(huì)比較少，而顧客買(mǎi)同樣的多的鎖產(chǎn)生的互開(kāi)次數(shù)越多顧客的不滿意度會(huì)增加。所以當(dāng)同一客戶買(mǎi)的鎖不超過(guò)98箱時(shí)，以第四中方案賣(mài)鎖最好。這里我們只稍微對(duì)其做下簡(jiǎn)單的解釋?zhuān)簩?duì)于奇偶交叉賣(mài)：同一客戶，當(dāng)買(mǎi)完49箱奇（或偶）時(shí)，每賣(mài)一個(gè)偶（或奇）的鎖是都會(huì)加至少4個(gè)互開(kāi)對(duì)數(shù)；而對(duì)與只賣(mài)奇（或偶）型的鎖時(shí)，當(dāng)賣(mài)完49箱時(shí)，每多賣(mài)一個(gè)奇（或偶）型鎖都只加一個(gè)互開(kāi)對(duì)數(shù)，所以這個(gè)方案來(lái)的比較優(yōu)。當(dāng)同一客戶買(mǎi)的所超過(guò)98箱的情況，同理我們可推出當(dāng)客戶買(mǎi)的鎖大于98時(shí)，買(mǎi)同一種類(lèi)型的鎖會(huì)來(lái)的好。六

20、.模型的評(píng)價(jià)與改進(jìn)1.我們所研究的是針對(duì)一個(gè)客戶的策略，本模型對(duì)于這個(gè)有較優(yōu)的適用性，具有一定的實(shí)際意義和參考性。2.在我們的模型假設(shè)中我們認(rèn)為顧客的抱怨度和互開(kāi)對(duì)百分比相等，但是當(dāng)模型的基數(shù)極大的時(shí)候，無(wú)疑這個(gè)假設(shè)是有一定誤差的。這個(gè)是值得進(jìn)一步改進(jìn)并加以推廣的。3模型在不忽略整體的情況下，從個(gè)體出發(fā)進(jìn)行分析，避免了陷入整體情況的討論。同時(shí)又能反映整體情況。七.參考文獻(xiàn)1 全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽委員會(huì)，全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽優(yōu)秀論文匯編，北京：中國(guó)物價(jià)出版社，20022 王樹(shù)禾，圖論，北京：科學(xué)出版社，20043 朱道元，數(shù)學(xué)建模案例精選，北京：科學(xué)出版社，2003八、附錄以下部分是本模型主

21、要代碼：clear"global*"a=tablei,j,k,l,m,i,1,6,j,1,6,k,1,6,l,1,6,m,1,6;b=flattena,4;p1=lengthunion#13&p2=lengthunion#14&p3=lengthunion#15&tableci=0,i,1,3;c1=selectb,p1;c2=selectb,p2;c3=selectb,p3;fori=1,i£3,i+,di=deletecasesdeletecasesci,_,1,6,_,_,6,1,_;n1=lengthd1n2=lengthd2n3=

22、lengthd3n=n1+n2+n3m=n/60g=joind1,d2,d3 2544 2808 528 5880 98由于5880種鎖，數(shù)據(jù)太大，這里就不不輸出，有意者可以將上面程序在mathematica中運(yùn)行。(*o,e分別為奇數(shù)和偶數(shù)鎖具*) o=selectg,oddqplus#&e=selectg,evenqplus#&lengtholengthe 2940 2940這里也沒(méi)給出o和e，有意者可運(yùn)行上面程序。 (*t為鎖的可以互開(kāi)數(shù),我們叫為匹配數(shù)*) t=0;fori=1,i£5880,i+,forj=1,j£5880,j+,ifsortgi-

23、gj0,0,0,0,1,t+;t 22778 tablewi=0,i,1,2940;fori=1,i£2940,i+,forj=1,j£2940,j+,ifsortabsoj-ei0,0,0,0,1,wi+;s=tablewi,i,1,2940;tablepi=positions,i,i,4,10;fori=4,i£10,i+,ui=extracte,pi;print"有",i,"個(gè)匹配數(shù),總共",lengthpi,".如下:"printui 有 4 個(gè)匹配數(shù),總共 45 .如下: 1,1,1,2,3,1

24、,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

25、,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 個(gè)匹配數(shù),總共 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,

26、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,

27、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,

28、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,

29、6,6,2,5,1 有 6 個(gè)匹配數(shù),總共 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

30、,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

31、,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

32、,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

33、,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

34、,5,6,6,3,6,5,6,6,6,3,6,2,1,1,2,6,2,1,2,1,6,2,2,1,1,6,2,2,6,4,6,2,3,3,6,6,2,3,6,3,6,2,4,2,6,6,2,4,6,2,6,2,4,6,6,6,2,6,2,4,6,2,6,3,3,6,2,6,4,6,6,2,6,6,4,6,3,1,1,1,6,3,2,6,3,6,3,3,2,6,6,3,3,6,2,6,3,5,6,6,6,3,6,2,3,6,3,6,5,6,6,3,6,6,5,6,4,2,6,2,6,4,2,6,6,6,4,6,2,6,6,4,6,6,2,6,5,3,6,6,6,5,5,5,1,6,5,6,3,6

35、,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

36、,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

37、,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

38、,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 個(gè)匹配數(shù),

39、總共 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,

40、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,

41、2,2,2,3,2,1,2,2,5,1,2,2,2,6,2,4,2,2,6,4,6,2,2,6,5,5,2,2,6,6,4,2,3,1,2,2,2,3,2,1,2,2,3,2,2,1,2,3,3,6,6,2,3,6,3,6,2,3,6,6,3,2,4,1,1,4,2,4,1,4,1,2,4,2,6,2,2,4,2,6,6,2,4,4,1,1,2,4,6,2,6,2,4,6,6,2,2,4,6,6,6,2,5,1,2,2,2,5,2,6,5,2,5,5,2,6,2,5,5,6,2,2,5,6,2,5,2,6,2,2,4,2,6,2,3,3,2,6,2,4,2,2,6,2,4,4,2,6,4,4,

42、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,

43、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,

44、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,

45、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,

46、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,

47、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,

48、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,

49、6,6,3,3,1,1,6,3,3,3,5,6,3,3,4,6,6,3,3,5,3,6,3,3,6,4,6,3,4,3,6,6,3,4,6,3,6,3,5,3,3,6,3,6,3,2,6,3,6,3,4,6,3,6,4,3,6,4,1,1,4,6,4,1,4,1,6,4,2,2,6,6,4,2,6,4,6,4,3,3,6,6,4,3,6,3,6,4,4,1,1,6,4,4,2,6,6,4,4,6,2,6,4,5,5,6,6,4,5,6,5,6,4,6,2,2,6,4,6,2,4,6,4,6,3,3,6,4,6,5,5,6,5,2,6,5,6,5,3,3,3,6,5,4,5,6,6,5,4,6,

50、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,

51、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