杭州交通信息网阳台对着三角形:数学竞赛英文的题
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5.(a) In a tiddlywinks tournament seven people play each other once,
with 2
points for a win, 1 point for a draw, and 0 points for a loss. During
the
tournament the players only know the results of their own games. How
may
points must a player score in order to be sure of finishing in the top
three(i.e. scoring more than at least four other players)?
(b) Suppose there are n players. how many points must one score in
order to
be sure of finishing in the top k?
请用中文解!!谢谢!!回答写详细点!!
with 2
points for a win, 1 point for a draw, and 0 points for a loss. During
the
tournament the players only know the results of their own games. How
may
points must a player score in order to be sure of finishing in the top
three(i.e. scoring more than at least four other players)?
(b) Suppose there are n players. how many points must one score in
order to
be sure of finishing in the top k?
请用中文解!!谢谢!!回答写详细点!!
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.