2000 AMC 8 Problem 9

Question

Three-digit powers of

2

and

5

are used in this “cross-number” puzzle. What is the only possible digit for the outlined square?

\begin{array}{lcl} \textbf{\text{ACROSS}} & & \textbf{\text{DOWN}} \\ \textbf{2. } 2^m & & \textbf{1. } 5^n \end{array}

0

2

4

6

8

List the three-digit powers of

5

The across entry is a three-digit power of

2

starting with

2

The only

3

-digit powers of

5

are

125

and

625.

This means that the

2

spot is filled with a

2.

The only

3

-digit power of

2

beginning with a

2

is

256,

so the outlined square is filled with a

6.

Thus, D is the correct answer.

Problem 9 in other years