Question

一个棋盘由 $64$ 个方格组成，阴影格和非阴影格交替排列。下图显示了底行的方格 $P$ 和顶行的方格 $Q$ 。一个标记放在 $P$ 上。一步是把标记移到上一行相邻的一个非阴影方格。从 $P$ 到 $Q$ 有多少条 $7$ 步路径？（图中显示了一条示例路径。）

A game board consists of $64$ squares that alternate between shaded and unshaded. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P.$ A step consists of moving the marker onto one of the adjoining unshaded squares in the row above. How many $7$ -step paths are there from $P$ to $Q?$ (The figure shows a sample path.)

$28$

$30$

$32$

$33$

$35$

答案：A

知识点：格路杨辉三角

难度评级：1460

视频讲解：

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文字解答：

每一步都必须从 $P$ 起向上一行，并向左或向右移动。逐行计算时，每个可达方格的路径数等于下面两个相邻方格路径数之和。

方格 $Q$ 处的计数是 $28$ ，所以共有 $28$ 条路径。

正确答案是 A。

Each move must go up one row and either left or right. Counting row by row from $P,$ each reachable square gets the sum of the counts from the two adjoining squares below it.

The count at $Q$ is $28,$ so there are $28$ paths.

Thus, the correct answer is A.

2020 AMC 8 第 21 题

答案：A

难度评级：1460

视频讲解：

文字解答：

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