2017 AMC 8 第 11 题
先试着解答 2017 AMC 8 第 11 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2017 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
11.
一个正方形地板由全等的正方形瓷砖铺成。如果位于两条对角线上的瓷砖总数是 ，那么铺满地板共有多少块瓷砖？
A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is how many tiles cover the floor?
小提示：
在奇数乘奇数的正方形中，两条对角线只共享中心瓷砖
In an odd-by-odd square, the two diagonals share exactly the center tile.
大提示：
如果每条对角线上有 块瓷砖，两条对角线合起来有 块
If each diagonal has tiles, the two diagonals together contain tiles.
视频讲解：
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文字解答：
两条对角线共有 块瓷砖，表示每条对角线上有 块瓷砖，因为中间有一块重叠。每行瓷砖数等于一条对角线上的瓷砖数，所以总瓷砖数为 。
所以正确答案是 C。
tiles on both diagonals imply that there are tiles on each diagonal, since one tile overlaps in the middle. The total number of tiles would then be since the number of tiles in each row is equal to the number of tiles in one diagonal.
Thus, C is the correct answer.
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