Question

数学竞赛英文的题

Answer 1

分类: 教育/学业/考试 >> 考研
问题描述:

5.(a) In a tiddlywinks tournament seven people play each other once,with 2points for a win, 1 point for a draw, and 0 points for a loss. Duringthetournament the players only know the results of their own games. Howmaypoints must a player score in order to be sure of finishing in the topthree(i.e. scoring more than at least four other players)?(b) Suppose there are n players. how many points must one score inorder tobe sure of finishing in the top k?请用中文解!!谢谢!!回答写详细点!!

解析:

a

积12分,全胜,一定是第1名;

积11分,平1局,最差是并列第1名;

积10分,输1局或平2局,最差是第2名;

积9分,输1局平1局或平3局,可能是第4名;

积8分,输2局或输1局平2局或平4局,可能是第4名;

故应当至少积10分,才能保证一定进前三.

b

积2n-2分,全胜,一定是第1名;

积2n-3分,平1局,最差是并列第1名;

积2n-4分,输1局或平2局,最差是第2名;

积2n-5分,输1局平1局或平3局,可能是第k+1名;

积2n-6分,输2局或输1局平2局或平4局,可能是第k+1名;

故应当至少积2n-4分,才能保证一定进前k.