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)高中 回應 isomorphism Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 2007-02-02 19:14 Part (a) is quite trivial since you can permute (2,3,4,...J,Q,K) 12! different ways. isomorphism Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 2007-02-02 19:40 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.
isomorphism Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 2007-02-02 19:14 Part (a) is quite trivial since you can permute (2,3,4,...J,Q,K) 12! different ways.
isomorphism Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題 2007-02-02 19:40 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.
回應
isomorphism
Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題
2007-02-02 19:14isomorphism
Re: 環球城市數學競賽2006秋季賽高中組高級卷第6題
2007-02-02 19:40