（原标题：概率问题）
来源:馨尹于06-12-1700:56:20
已知13个数字中任选3个数字的组合是286组，13个数字中任选6个数字的组合是1716组，请问选6个数字的组合中最少几组就可以包含所有选3的组合？
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Deuss:
35个可以，不知能否更少
split13elementsinto7groups:[1,2],[3,4]...[11,12],[13].
formsize6groupsbypickingall3-combinationsfromthese7,(addanyoneadditiona...[阅读全文]
博文
(2006-12-17 11:43:03)
(2006-12-10 11:30:45)
(2006-12-08 14:21:55)
来源:haha2000于06-12-0811:42:26Provetheinequalityfornumbersa---------------Deuss:inductionworks,butalittleclumsycanassumea=1,otherwisedividingallxibya.[阅读全文]
(2006-12-07 14:06:19)
triangleareainequality
来源:haha2000于06-12-0413:05:58
ThisisanoldproblemIknewmanyyearsago.Ihopewhatisinmymemoryisstillgood:).T1isatrianglewithsidelength,a1,b1,andc1.
T2isatrianglewithsidelength,a2,b2,andc2.T3isatrianglewithsidelength,a1+a2,b1+b2,andc1+c2.(Itisnothardtoshowthat:a1+a2,b1+b2,andc1+c2canformatriangle.)Thereisaninterestinginequityamongareasofthethreetriangles.Let...[阅读全文]
来源:haha2000于06-12-0413:05:58
ThisisanoldproblemIknewmanyyearsago.Ihopewhatisinmymemoryisstillgood:).T1isatrianglewithsidelength,a1,b1,andc1.
T2isatrianglewithsidelength,a2,b2,andc2.T3isatrianglewithsidelength,a1+a2,b1+b2,andc1+c2.(Itisnothardtoshowthat:a1+a2,b1+b2,andc1+c2canformatriangle.)Thereisaninterestinginequityamongareasofthethreetriangles.Let...[阅读全文]
(2006-11-17 19:30:17)
(2006-11-11 04:28:56)
来源:constant于06-11-0908:07:29设有n块相同的砖，在一张桌子的边上一块一块的垒起来（每层一块）。问最远的一块能伸出桌边多远？要证明不能更远了。
Deuss:(1+1/2+1/3+…+1/n)/2.Assumeabrickhaslength1,thecornerofthetableisatposition0.
Bricksarenumberedtopdownas1,2,...,n
LetP_kbethecenterpositionofthek-thbrick,
andQ_kbetheweightcenterofthefirstkbricks.
Toreachfarthest,thefollowingrelation...[阅读全文]
Deuss:(1+1/2+1/3+…+1/n)/2.Assumeabrickhaslength1,thecornerofthetableisatposition0.
Bricksarenumberedtopdownas1,2,...,n
LetP_kbethecenterpositionofthek-thbrick,
andQ_kbetheweightcenterofthefirstkbricks.
Toreachfarthest,thefollowingrelation...[阅读全文]
(2006-10-24 21:04:30)
问题来源:haha2000于06-10-2413:56:08
Givenajar,thereare10redcandies,20bluecandies,30greencandies,whatistheprobabilitythatthereareatleast1bluecandyand1greencandyleftinthejarwhenyouhavetakenalltheredcandiesout?
Deuss:7/12
Therearetotally60!Permutations.
NowcountthoseendwithRG*orRB*,where*means0ormoreoccurrencesoftheprecedingcolor.
Ingeneral,assumem+n+1numberedballs,withmofcolorX,1...[阅读全文]
Givenajar,thereare10redcandies,20bluecandies,30greencandies,whatistheprobabilitythatthereareatleast1bluecandyand1greencandyleftinthejarwhenyouhavetakenalltheredcandiesout?
Deuss:7/12
Therearetotally60!Permutations.
NowcountthoseendwithRG*orRB*,where*means0ormoreoccurrencesoftheprecedingcolor.
Ingeneral,assumem+n+1numberedballs,withmofcolorX,1...[阅读全文]
(2006-10-20 19:54:31)
1.ithaseverything,convenient
2.manymanypeoplehere,youfeeltheprosperity
3.manymanybusinesshere,easytofindajob
4.muchmuchmoneyhere--notmine--butstill,goodlivinghere
5.nottoohot,nottoocold
6.noearthquake,nohurricane
7.bytheAppalachianMountains,bytheAtlanticOcean,acoupleofbeautifulrivers
8.youdon'thavetoownacarifyouchoosenotto
9.easytogoanywherefromhere
10.even...[阅读全文]
(2006-10-19 20:25:29)
来源:馨尹于06-10-1917:57:15
设有一条绳子(很好的橡皮绳)长1米,而且每秒均匀拉伸10厘米,
一只虫子(当然是理想的虫子啦,永远不死的虫子,)从绳子的一端爬向
另一端,每秒爬1厘米,
问,虫子能爬到另一端否?
Deuss:Thisisthecontinuousversionoftheproblem.Otherpeoplealreadypresentedsolutions.Hereweusetheideaofmeasuringthedistanceintheoriginalrope,i.e.atanymoment,wecanimaginetoscalebacktheropetoorigin...[阅读全文]
(2006-10-15 13:32:46)
TriangleABChsaitsbaseonlinesegmentPNandvertexAonlinePM.CircleswithcentresOandQ,havingradiir1andr2,respectively,aretangenttothetriangleABCexternallyatpointKandLandtoeachofPMandPN.
(a)ProvethatthelinethroughKandLcutstheperimeteroftriangleABCintotwoequalpieces.
(b)LetTbethepointofcontactofBCwiththecircleinscribedintriangleABC.Provethat(TC)(r1)+(TB)(r2)isequaltotheareaoftriangleABC.
Proof:...[阅读全文]
