2024 AMC 8 第 17 题
先试着解答 2024 AMC 8 第 17 题，然后核对你的答案与精心整理的解答，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 2024 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。
17.
国际象棋中的王会攻击水平、竖直或对角方向相邻一步的所有方格。例如，在 网格中心方格上的王会攻击其他 个方格，如下图所示。若一个白王和一个黑王放在 网格的不同方格上，并且它们互不攻击，有多少种放法？
A chess king is said to attack all the squares one step away from it, horizontally, vertically, or diagonally. For instance, a king on the center square of a grid attacks all other squares, as shown below. Suppose a white king and a black king are placed on different squares of a grid so that they do not attack each other. In how many ways can this be done?
小提示：
先按白王的位置分类计数
Count ordered placements for the white king first
大提示：
角落给黑王 个安全格；边中格给 个安全格
A corner allows safe black-king squares; an edge-center allows
解答：
先选白王所在方格。若白王在中心，它攻击所有其他方格，黑王有 个可放位置。
若白王在角落，它攻击 个方格，黑王有 个安全格。角落有 个，所以共有 种。
若白王在边上但不是角落，它攻击 个方格，黑王有 个安全格。这样的边中格有 个，所以共有 种。
总数为 。
所以正确答案是 E。
Count ordered placements by first choosing the square for the white king. If the white king is in the center, it attacks every other square, so there are choices for the black king.
If the white king is in a corner, it attacks squares, so the black king has safe squares. There are corner choices, giving placements.
If the white king is on an edge but not a corner, it attacks squares, so the black king has safe squares. There are such edge choices, giving placements.
The total number of placements is .
Thus, E is the correct answer.
其他年份的第 17 题
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