1992 AMC 12 第 8 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。
8.
一个正方形地面由全等的正方形瓷砖铺成。两条对角线上的瓷砖是黑色的，其余瓷砖是白色的。若共有 块黑色瓷砖，则瓷砖总数为
A square floor is tiled with congruent square tiles. The tiles on the two diagonals of the floor are black. The rest of the tiles are white. If there are black tiles, then the total number of tiles is
答案：E
小提示：
若地面每边有 块瓷砖，计算两条对角线上的瓷砖数
If the floor has tiles on a side, count the tiles on both diagonals
大提示：
由于黑色瓷砖总数为奇数，两条对角线共用中央的一块瓷砖
Because the total number of black tiles is odd, the two diagonals share one center tile
解答：
当 为奇数时，每条对角线含有 块瓷砖，两条对角线只共用中央的一块。因此 ，所以 。地面共有 块瓷砖。
因此正确答案是 E。
For an odd each diagonal contains tiles and the two diagonals share only the center tile. Hence so The floor therefore contains tiles.
Thus the correct answer is E.
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