發布者 | 內容列 | 訪客
| 環球城市數學競賽2006秋季賽高中組高級卷第6題 | | 6. 有一疊52張的撲克牌,若黑桃A在這疊牌的最上方且任何相鄰的二張牌其點數或是花色相同(這疊牌最上方的牌和最下方的牌也視為相鄰),則稱這疊牌排列的順序為「整齊的順序」。已知將這疊牌排成「整齊的順序」的方法數為n種,試證: (a) n可被12!整除。(三分) (b) n可被13!整除。(五分)
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| 2006-11-06 10:11 | | isomorphism Not too shy to talk
註冊日: 2007-01-30 發表數: 40
| Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 | | Part (a) is quite trivial since you can permute (2,3,4,...J,Q,K) 12! different ways. |
| 2007-02-02 19:14 | | isomorphism Not too shy to talk
註冊日: 2007-01-30 發表數: 40
| Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 | | Actually part (b) is also quite trivial. Just consider permutations of (A,2,3,4,5,...,Q,K). Even though the A is shifted to a new position, the 52 cycle is still different from previous cycles.
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| 2007-02-02 19:40 | |
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