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[求助] 数学逻辑问题求助

各位万能的虫友,求助这道题怎么破呀
N/2 of the N people were men and N/2 were women. Show that it is possible, without reseating anyone, to draw N/2 lines across the circular table  joining each woman to a different man  in such a way that none of the lines intersect.
一共有N个人绕圆桌而坐(在一条线上不会同时有三个人),男女各一半,在不移动任何人位置的前提下,画N/2条线,使每个女性对应一位男性(一对一,不能一对多或多对一),试说明这N/2条线存在不不相交的情况
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