2018 AMC 8 第 9 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。
9.
Tyler 正在给他 英尺乘 英尺的客厅铺地砖。他计划沿房间边缘用一英尺乘一英尺的正方形地砖铺一圈边框，其余部分用二英尺乘二英尺的正方形地砖铺满。他一共会用多少块地砖？
Tyler is tiling the floor of his foot by foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?
小提示：
先数 英尺宽边框上的地砖，注意角落不要重复计算
Count the -foot border tiles first, being careful not to double-count the corners.
大提示：
去掉一圈 英尺边框后，剩余矩形是 英尺乘 英尺
After removing a -foot border, the remaining rectangle is feet by feet.
视频讲解：
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文字解答：
注意边框每平方英尺需要一块地砖，所以四边相加会得到 块。不过这样四个角各重复计算了一次，所以要减去 。因此边框共需要 块 正方形地砖。
由于每边都去掉了一英尺宽的边框，剩下的内部矩形为 英尺乘 英尺。它要完全铺上 的地砖，所以这部分需要 块地砖。
边框需要 块 地砖，内部需要 块 地砖，因此一共需要 块地砖。
所以正确答案是 B。
Note that each square foot of the border would require one tile, meaning that the border will take tiles. However, notice that this will cause overlapping tiles in each of the four corners, so to fix this, we subtract Therefore, the border will take square tiles to completely tile.
Since we have removed one foot from each side due to the border, the remaining rectangle is feet by feet. This must be tiled completely by tiles, so it will take tiles in total to tile this area.
As it takes square tiles to tile the border, and square tiles to tile the remaining area, it will take tiles in total to fill in Tyler’s entire living room floor.
Thus, the correct answer is B.
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