# Difference between revisions of "2000 AMC 8 Problems/Problem 9"

## Problem

Three-digit powers of $2$ and $5$ are used in this cross-number puzzle. What is the only possible digit for the outlined square? $$\begin{array}{lcl} \textbf{ACROSS} & & \textbf{DOWN} \\ \textbf{2}. 2^m & & \textbf{1}. 5^n \end{array}$$

$[asy] draw((0,-1)--(1,-1)--(1,2)--(0,2)--cycle); draw((0,1)--(3,1)--(3,0)--(0,0)); draw((3,0)--(2,0)--(2,1)--(3,1)--cycle,linewidth(1)); label("1",(0,2),SE); label("2",(0,1),SE); [/asy]$

$\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

## Solution

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 $\boxed{\text{(D) 6}}$.

 2000 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 8 Followed byProblem 10 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions