（原標題：概率問題）
來源:馨尹於06-12-1700:56:20
已知13個數字中任選3個數字的組合是286組，13個數字中任選6個數字的組合是1716組，請問選6個數字的組合中最少幾組就可以包含所有選3的組合？
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Deuss:
35個可以，不知能否更少
split13elementsinto7groups:[1,2],[3,4]...[11,12],[13].
formsize6groupsbypickingall3-combinationsfromthese7,(addanyoneadditiona...[閱讀全文]
博文
(2006-12-17 11:43:03)
(2006-12-10 11:30:45)
(2006-12-08 14:21:55)
來源:haha2000於06-12-0811:42:26Provetheinequalityfornumbersa---------------Deuss:inductionworks,butalittleclumsycanassumea=1,otherwisedividingallxibya.[閱讀全文]
(2006-12-07 14:06:19)
triangleareainequality
來源:haha2000於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...[閱讀全文]
來源:haha2000於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...[閱讀全文]
(2006-11-17 19:30:17)
(2006-11-11 04:28:56)
來源:constant於06-11-0908:07:29設有n塊相同的磚，在一張桌子的邊上一塊一塊的壘起來（每層一塊）。問最遠的一塊能伸出桌邊多遠？要證明不能更遠了。
Deuss:(1+1/2+1/3+…+1/n)/2.Assumeabrickhaslength1,thecornerofthetableisatposition0.
Bricksarenumberedtopdownas1,2,...,n
LetP_kbethecenterpositionofthek-thbrick,
andQ_kbetheweightcenterofthefirstkbricks.
Toreachfarthest,thefollowingrelation...[閱讀全文]
Deuss:(1+1/2+1/3+…+1/n)/2.Assumeabrickhaslength1,thecornerofthetableisatposition0.
Bricksarenumberedtopdownas1,2,...,n
LetP_kbethecenterpositionofthek-thbrick,
andQ_kbetheweightcenterofthefirstkbricks.
Toreachfarthest,thefollowingrelation...[閱讀全文]
(2006-10-24 21:04:30)
問題來源:haha2000於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...[閱讀全文]
Givenajar,thereare10redcandies,20bluecandies,30greencandies,whatistheprobabilitythatthereareatleast1bluecandyand1greencandyleftinthejarwhenyouhavetakenalltheredcandiesout?
Deuss:7/12
Therearetotally60!Permutations.
NowcountthoseendwithRG*orRB*,where*means0ormoreoccurrencesoftheprecedingcolor.
Ingeneral,assumem+n+1numberedballs,withmofcolorX,1...[閱讀全文]
(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...[閱讀全文]
(2006-10-19 20:25:29)
來源:馨尹於06-10-1917:57:15
設有一條繩子(很好的橡皮繩)長1米,而且每秒均勻拉伸10厘米,
一隻蟲子(當然是理想的蟲子啦,永遠不死的蟲子,)從繩子的一端爬向
另一端,每秒爬1厘米,
問,蟲子能爬到另一端否?
Deuss:Thisisthecontinuousversionoftheproblem.Otherpeoplealreadypresentedsolutions.Hereweusetheideaofmeasuringthedistanceintheoriginalrope,i.e.atanymoment,wecanimaginetoscalebacktheropetoorigin...[閱讀全文]
(2006-10-15 13:32:46)
TriangleABChsaitsbaseonlinesegmentPNandvertexAonlinePM.CircleswithcentresOandQ,havingradiir1andr2,respectively,aretangenttothetriangleABCexternallyatpointKandLandtoeachofPMandPN.
(a)ProvethatthelinethroughKandLcutstheperimeteroftriangleABCintotwoequalpieces.
(b)LetTbethepointofcontactofBCwiththecircleinscribedintriangleABC.Provethat(TC)(r1)+(TB)(r2)isequaltotheareaoftriangleABC.
Proof:...[閱讀全文]
