1959 AMC 12 第 50 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
50.
一个有 名成员的俱乐部按以下两条规则组成四个委员会：
每名成员属于且只属于两个委员会。
任意两个委员会恰有一名共同成员。
则 ：
A club with members is organized into four committees in accordance with these two rules:
Each member belongs to two and only two committees.
Each pair of committees has one and only one member in common.
Then
无法确定
cannot be determined
在 与 之间恰有一个值
has a single value between and
在 与 之间有两个值
has two values between and
在 与 之间恰有一个值
has a single value between and
在 与 之间有两个值
has two values between and
小提示：
将每名成员与其所属的两个委员会组成的无序对对应
Associate each member with the pair of committees to which that member belongs
大提示：
规则 表明四个委员会中的每一对恰好出现一次
Rule says every pair of the four committees occurs exactly once
解答：
每名成员恰好对应一对无序的委员会。反之，每对委员会恰有一名共同成员。因此成员与四个委员会的两两组合一一对应，所以 这是 与 之间的唯一值。
因此，正确答案是 D。
Each member belongs to exactly one unordered pair of committees. Conversely, each pair of committees has exactly one common member. Thus the members are in one-to-one correspondence with the pairs of four committees, so This is a single value between and
Therefore, the correct answer is D.