AMC8 1993

AMC8 1993 · Q25

AMC8 1993 · Q25. It mainly tests Area & perimeter, Geometric probability (basic).

A checkerboard consists of one-inch squares. A square card, 1.5 inches on a side, is placed on the board so that it covers part or all of the area of each of n squares. The maximum possible value of n is

一个棋盘由一英寸见方的方格组成。一个边长 1.5 英寸的方形卡片放在棋盘上，使得它覆盖了 n 个方格的部分或全部区域。n 的最大可能值是

(A) 4 or 5 4 或 5

(B) 6 or 7 6 或 7

(D) 10 or 11 10 或 11

(E) 12 or more 12 或更多

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): Using the Pythagorean Theorem, the length of the diagonal of the card is $\sqrt{(1.5)^2 + (1.5)^2} = \sqrt{4.5} \approx 2.1$. This is longer than 2, the length of two adjacent squares. The figure shows 12 squares being touched.

答案（E）：使用勾股定理，卡片对角线的长度为 $\sqrt{(1.5)^2 + (1.5)^2} = \sqrt{4.5} \approx 2.1$。这比 2（两个相邻方格的边长之和）更长。图中显示有 12 个方格被触及。

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