2000 AMC 8 竞赛试题/第8题
Problem
Three-digit powers of 
and 
are used in this cross-number puzzle. What is the only possible digit for the outlined square?![\[\begin{array}{lcl} \textbf{ACROSS} & & \textbf{DOWN} \\ \textbf{2}. 2^m & & \textbf{1}. 5^n \end{array}\]](/ueditor/php/upload/image/20180417/1523949211221828.png)
![[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]](/ueditor/php/upload/image/20180417/1523949212741257.png)
Solution
The 
-digit powers of are 
and 
, so space is filled with a . The only -digit power of beginning with is 
, so the outlined block is filled with a 
.
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