1968 AMC 12 第 19 题
先试着解答 1968 AMC 12 第 19 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 1968 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。
19.
将 美元兑换成一角硬币和二角五分硬币，且每种硬币至少使用一枚。设兑换方法数为 ，则 等于：
Let be the number of ways that dollars can be changed into dimes and quarters, with at least one of each coin being used. Then equals:
小提示：
以美分为单位，求解
In cents, solve
大提示：
利用奇偶性写成 ，再要求两种硬币的枚数均为正数
Use parity to write , then enforce positive coin counts
解答：
方程 化简为 。因此 必须为偶数；令 ，则 。由两者均为正数可得 、、、，所以共有 种方法。
因此，正确答案是 E。
The equation reduces to Thus must be even; write giving Positivity requires so there are ways.
Therefore, the correct answer is E.
其他年份的第 19 题
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