1990 AMC 12 第 17 题
先试着解答 1990 AMC 12 第 17 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 1990 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。
17.
从 、、、 中，有多少个数的三个数字互不相同，并且按递增或递减顺序排列？
How many of the numbers have three different digits in increasing order or in decreasing order?
答案：C
小提示：
选定三个不同的数字后，它们的递增顺序或递减顺序就唯一确定
Choosing three distinct digits fixes their increasing or decreasing order
大提示：
在递增情形中，要谨慎处理数字
Treat the digit carefully in the increasing case
解答：
递增的三位数不能使用 ，所以递增数共有 个。从 到 中任取三个数字，都能组成一个有效的递减三位数，因为最大的数字位于首位；这样的数有 个。总数为 。
所以正确答案是 C。
An increasing three-digit number cannot use so there are increasing numbers. Any three digits chosen from through form a valid decreasing three-digit number, because the largest digit comes first; this gives The total is
Thus the correct answer is C.
其他年份的第 17 题
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