2024 AMC 8 第 23 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。
23.
Rodrigo 有一张很大的方格纸。首先，他画一条线段连接点 与点 ，并给线段内部穿过的 个方格涂色，如下图所示。接着，Rodrigo 画一条线段连接点 与点 。他同样给线段内部穿过的方格涂色。这次他会涂多少个方格？
Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point to point and colors the cells whose interiors intersect the segment, as shown below. Next, Rodrigo draws a line segment connecting point to point Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?
小提示：
对端点坐标差为 和 的线段，数它穿过的格子
For a segment with integer endpoint differences and , count grid cells crossed
大提示：
使用 计算内部被线段穿过的方格数
Use for cells whose interiors are intersected
视频讲解：
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文字解答：
若线段水平差为 、竖直差为 ，它穿过 条竖直网格线和 条水平网格线，但在格点处的穿越会被重复计算。因此内部被线段穿过的方格数为
这里坐标差为 和 ，且 。所以方格数为
正确答案是 C。
For a segment whose endpoint differences are horizontally and vertically, the segment crosses vertical grid lines and horizontal grid lines, but crossings at lattice points are counted twice. Therefore the number of cells whose interiors are intersected is
Here the endpoint differences are and , and . Thus the number of cells colored is
Thus, C is the correct answer.
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