tag:blogger.com,1999:blog-3550204829234352390.post8629912239537661424..comments2024-03-27T09:13:48.546+08:00Comments on 研發養成所 ( Bridan's Blog - 4rdp, For R&D Person ): Hints on Total 22Bridanhttp://www.blogger.com/profile/17055047757114667099noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3550204829234352390.post-20636964662927048962016-01-07T23:34:06.299+08:002016-01-07T23:34:06.299+08:00這題放了近兩年半,終於有人提出"重複"的解法,不過正解要計算到 n(0),208...這題放了近兩年半,終於有人提出"重複"的解法,不過正解要計算到 n(0),2083841<br />雖然少算一個步驟,方老師還是很厲害,從看到題目到寫出解法不到一天的時間,我還沒有這樣的功力Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-83862922221095115062016-01-07T21:06:01.197+08:002016-01-07T21:06:01.197+08:00對於可重覆的方法數,我的想法是:
最左邊的數可能是1,也可能是2,…,也可能是10。
所以若令加起來...對於可重覆的方法數,我的想法是:<br />最左邊的數可能是1,也可能是2,…,也可能是10。<br />所以若令加起來的數是k時的分法共有N(k)種方法 (可重覆,即10, 10, 2 與 10, 2, 10看作不同分法)<br />則n(k)=n(k-1)+ n(k-2)+ n(k-3)+ n(k-4)+ n(k-5)+ n(k-6)+ n(k-7)+ n(k-8)+ n(k-9)+ n(k-10) <br />故所求=n(22)<br /> =n(21)+ n(20)+ n(19)+ n(18)+ n(17)+ n(16)+ n(15)+ n(14)+ n(13)+ n(12)<br /> =2(n(20)+ n(19)+ n(18)+ n(17)+ n(16)+ n(15)+ n(14)+ n(13)+ n(12))+n(11)<br /> =4(n(19)+ n(18)+ n(17)+ n(16)+ n(15)+ n(14)+ n(13)+ n(12))+3n(11)+2n(10)<br /> =8(n(18)+ n(17)+ n(16)+ n(15)+ n(14)+ n(13)+ n(12))+7n(11)+6n(10)+4n(9)<br /> =16(n(17)+ n(16)+ n(15)+ n(14)+ n(13)+ n(12))+15n(11)+14n(10)+12n(9)+8n(8)<br /> =32(n(16)+ n(15)+ n(14)+ n(13)+ n(12))+31n(11)+30n(10)+28n(9)+24n(8)+16n(7)<br /> =64(n(15)+ n(14)+ n(13)+ n(12))+63n(11)+62n(10)+60n(9)+64n(8)+48n(7)+32n(6)<br /> =128(n(14)+ n(13)+ n(12))+127n(11)+126n(10)+124n(9)+120n(8)+112n(7)+96n(6)+64n(5)<br /> =256(n(13)+ n(12))+255n(11)+254n(10)+252n(9)+248n(8)+240n(7)+224n(6)+192n(5)+128n(4)<br /> =512n(12)+511n(11)+ 510n(10)+508n(9)+ 504n(8)+ 496n(7)+ 480n(6)+ 448n(5)+ 384n(4)+256n(3)<br /> =1023n(11)+ 1022n(10)+ 1020n(9)+ 1016n(8)+ 1008n(7)+ 992n(6)+960n(5)+ 896n(4)+ 768n(3)+ 512n(2)<br /> = 2045n(10)+ 2043n(9)+ 2039n(8)+ 2031n(7)+ 2015n(6)+1983n(5)+ 1919n(4)+ 1791n(3)+ 1535n(2)+1023n(1)<br />=4088n(9)+ 4084n(8)+ 4076n(7)+ 4060n(6)+4028n(5)+ 3964n(4)+ 3836n(3)+ 3580n(2)+3068n(1)<br />=8172n(8)+ 8164n(7)+ 8148n(6)+8116n(5)+ 8052n(4)+ 7924n(3)+ 7668n(2)+7156n(1)<br />=16336n(7)+ 16320n(6)+16288n(5)+ 16224n(4)+ 16096n(3)+ 15840n(2)+15328n(1)<br />=32656n(6)+32624n(5)+ 32560n(4)+ 32432n(3)+ 32176n(2)+31664n(1)<br />=65280n(5)+ 65216n(4)+ 65088n(3)+ 64832n(2)+64320n(1)<br />=130496n(4)+ 130368n(3)+130112n(2)+129600n(1)<br />=260864n(3)+260608n(2)+260096n(1)<br />=521472n(2)+520960n(1)<br />=1042432n(1)<br />=1042432<br /><br />所以共有1042432 方法。<br />Anonymoushttps://www.blogger.com/profile/13070867625558052970noreply@blogger.com