2026 AMC 8 第 20 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。
20.
Catania 有两种硬币：金币厚 毫米，银币厚 毫米。用这些硬币堆成高度为 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 mm thick and silver coins are mm thick. In how many ways can Taylor make a stack of coins that is mm tall using any arrangement of gold and silver coins, assuming order matters?
小提示：
按银币的个数分类。
Count by the number of silver coins
大提示：
如果有 枚银币，就要排列 枚银币和 枚金币。
With silver coins, arrange S’s and G’s
视频讲解：
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文字解答：
按银币数分类。没有银币时有 种；有一枚银币时，还有 枚金币和 枚银币，共 种排列；有两枚银币时，还有 枚金币和 枚银币，共 种排列。更多银币会太厚。总数为 。
Count by the number of silver coins. With no silver coins, there is stack. With one silver coin, there are gold coins and silver coin, so arrangements. With two silver coins, there are gold coins and silver coins, so arrangements. More silver coins are too thick. The total is .
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