Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2003 AMC 8 Problems/Problem 13"

(→‎solution)
Line 1: Line 1:
−
==solution==
+
==Problem==
 +
Fourteen white cubes are put together to form the fi gure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
 +
 
 +
<asy>
 +
import three;
 +
defaultpen(linewidth(0.8));
 +
real r=0.5;
 +
currentprojection=orthographic(3/4,8/15,7/15);
 +
draw(unitcube, white, thick(), nolight);
 +
draw(shift(1,0,0)*unitcube, white, thick(), nolight);
 +
draw(shift(2,0,0)*unitcube, white, thick(), nolight);
 +
draw(shift(0,0,1)*unitcube, white, thick(), nolight);
 +
draw(shift(2,0,1)*unitcube, white, thick(), nolight);
 +
draw(shift(0,1,0)*unitcube, white, thick(), nolight);
 +
draw(shift(2,1,0)*unitcube, white, thick(), nolight);
 +
draw(shift(0,2,0)*unitcube, white, thick(), nolight);
 +
draw(shift(2,2,0)*unitcube, white, thick(), nolight);
 +
draw(shift(0,3,0)*unitcube, white, thick(), nolight);
 +
draw(shift(0,3,1)*unitcube, white, thick(), nolight);
 +
draw(shift(1,3,0)*unitcube, white, thick(), nolight);
 +
draw(shift(2,3,0)*unitcube, white, thick(), nolight);
 +
draw(shift(2,3,1)*unitcube, white, thick(), nolight);
 +
</asy>
 +
 
 +
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12 </math>
 +
 
 +
==Solution==
 
We can see that there are only <math> \textbf{(B)6}</math> cubes by counting.
 
We can see that there are only <math> \textbf{(B)6}</math> cubes by counting.
 +
 +
{{AMC8 box|year=2003|num-b=12|num-a=14}}

Revision as of 10:07, 25 November 2011

Problem

Fourteen white cubes are put together to form the fi gure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?

[asy] import three; defaultpen(linewidth(0.8)); real r=0.5; currentprojection=orthographic(3/4,8/15,7/15); draw(unitcube, white, thick(), nolight); draw(shift(1,0,0)*unitcube, white, thick(), nolight); draw(shift(2,0,0)*unitcube, white, thick(), nolight); draw(shift(0,0,1)*unitcube, white, thick(), nolight); draw(shift(2,0,1)*unitcube, white, thick(), nolight); draw(shift(0,1,0)*unitcube, white, thick(), nolight); draw(shift(2,1,0)*unitcube, white, thick(), nolight); draw(shift(0,2,0)*unitcube, white, thick(), nolight); draw(shift(2,2,0)*unitcube, white, thick(), nolight); draw(shift(0,3,0)*unitcube, white, thick(), nolight); draw(shift(0,3,1)*unitcube, white, thick(), nolight); draw(shift(1,3,0)*unitcube, white, thick(), nolight); draw(shift(2,3,0)*unitcube, white, thick(), nolight); draw(shift(2,3,1)*unitcube, white, thick(), nolight); [/asy]

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12$

Solution

We can see that there are only $\textbf{(B)6}$ cubes by counting.

2003 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
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
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2003_AMC_8_Problems/Problem_13&oldid=43267"