Question

Catania 有两种硬币：金币厚 $1$ 毫米，银币厚 $3$ 毫米。用这些硬币堆成高度为 $8$ 毫米的一摞共有多少种方法？硬币的上下顺序不同算不同方法。

The land of Catania uses gold coins and silver coins. Gold coins are $1$ mm thick and silver coins are $3$ mm thick. In how many ways can Taylor make a stack of coins that is $8$ mm tall using any arrangement of gold and silver coins, assuming order matters?

$3$

$7$

$10$

$13$

$16$

答案：D

知识点：分拆与有序分拆组合分类讨论

难度评级：1510

视频讲解：

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文字解答：

按银币数分类。没有银币时有 $1$ 种；有一枚银币时，还有 $5$ 枚金币和 $1$ 枚银币，共 $6$ 种排列；有两枚银币时，还有 $2$ 枚金币和 $2$ 枚银币，共 $\binom42=6$ 种排列。更多银币会太厚。总数为 $1+6+6=13$ 。

Count by the number of silver coins. With no silver coins, there is $1$ stack. With one silver coin, there are $5$ gold coins and $1$ silver coin, so $6$ arrangements. With two silver coins, there are $2$ gold coins and $2$ silver coins, so $\binom42=6$ arrangements. More silver coins are too thick. The total is $1+6+6=13$ .

2026 AMC 8 第 20 题

答案：D

难度评级：1510

视频讲解：

文字解答：

其他年份的第 20 题