AMC8 2017

AMC8 2017 · Q15

AMC8 2017 · Q15. It mainly tests Basic counting (rules of product/sum), Geometry misc.

In the arrangement of letters and numerals below, by how many different paths can you spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.

在下面的字母和数字排列中，有多少条不同的路径可以拼出AMC8？从中间的A开始，路径只能移动到相邻的（上下左右，但不包括对角线）字母。图中描画了一条这样的路径示例。

(A) 8 8

(B) 9 9

(D) 24 24

(E) 36 36

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Starting at A, there are 4 choices for the M, each of which is followed by 3 choices for the C, each of which is followed by 2 choices for the 8. So all together, there are $4 \cdot 3 \cdot 2 = 24$ paths.

答案 (D)：从 A 出发，M 有 4 个选择，每个之后 C 有 3 个选择，每个之后 8 有 2 个选择。因此共有 $4 \cdot 3 \cdot 2 = 24$ 条路径。

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