2005 AMC 8 第 5 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。
5.
汽水以 、 和 罐装出售。要正好买 罐汽水，最少需要多少包？
Soda is sold in packs of and cans. What is the minimum number of packs needed to buy exactly cans of soda?
答案：B
小提示：
在总数不超过 的情况下尽量多用 罐装
Use as many -packs as possible without going over .
大提示：
三包 罐装后，用最少包数补齐剩余罐数
After three -packs, finish the remaining cans with the fewest packs.
解答：
四包不可能够用。四个 罐装共有 罐，把其中任意一个 罐装换成较小的包装，罐数会减少 或 。因此不可能恰好从 减少 罐而得到 罐。
五包可以做到：三个 罐装、一个 罐装和一个 罐装共有 罐。因此最少需要 包。
所以正确答案是 B。
Four packs cannot be enough. Four -packs would contain cans, and replacing any -pack by a smaller pack decreases the total by either or cans. There is no way to decrease by exactly cans to reach .
Five packs do work: three -packs, one -pack, and one -pack contain cans. Therefore, the minimum number is .
Thus, B is the correct answer.
其他年份的第 5 题
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