1995 AMC 12 第 29 题
先试着解答 1995 AMC 12 第 29 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1995 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
29.
有多少个由三个正整数组成的集合 满足 ？
For how many three-element sets of positive integers is it true that
答案：C
小提示：
将 分解为互不相同的质因数，并把每个质因数分配给一个因数
Factor into distinct primes and assign each prime to one of the factors
大提示：
分别统计一个因数为 以及三个因数都大于 的情形
Count separately the cases in which one factor is and in which all three factors exceed
解答：
因为 ，每个质因数恰好属于三个因数中的一个。若三个因数都大于 ，它们对应的无序质因数组就是把五个对象分成三个非空组，其数量为 若有一个因数为 ，则把这些质因数分成两个非空组，得到 。由于互不相交的质因数集合不同，所得因数也互不相同。因此总数为 ，正确答案是 C。
Since each prime belongs to exactly one of the three factors. If all factors exceed their unordered prime groups form a partition of five objects into three nonempty blocks, counted by If one factor is the primes are partitioned into two nonempty blocks, giving The factors are distinct because their disjoint prime sets differ. Thus the total is and the correct answer is C.
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