AMC8 2000

AMC8 2000 · Q9

AMC8 2000 · Q9. It mainly tests Perfect squares & cubes, Powers & residues.

Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square? ACROSS 2. $2^m$ DOWN 1. $5^n$

这个填字谜中使用三位数的 2 和 5 的幂。虚线方框的唯一可能数字是？ ACROSS 2. $2^m$ DOWN 1. $5^n$

(A) 0 0

(B) 2 2

(D) 6 6

(E) 8 8

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The 3-digit powers of 5 are 125 and 625, so space 2 is filled with a 2. The only 3-digit power of 2 beginning with 2 is 256, so the outlined block is filled with a 6.

答案（D）：5 的三位数幂是 125 和 625，所以第 2 个空格填 2。以 2 开头的唯一三位数的 2 的幂是 256，所以框出的方格填 6。

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