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

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==solution==
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==Problem==
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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?
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<asy>
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import three;
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defaultpen(linewidth(0.8));
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real r=0.5;
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currentprojection=orthographic(3/4,8/15,7/15);
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draw(unitcube, white, thick(), nolight);
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draw(shift(1,0,0)*unitcube, white, thick(), nolight);
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draw(shift(2,0,0)*unitcube, white, thick(), nolight);
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draw(shift(0,0,1)*unitcube, white, thick(), nolight);
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draw(shift(2,0,1)*unitcube, white, thick(), nolight);
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draw(shift(0,1,0)*unitcube, white, thick(), nolight);
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draw(shift(2,1,0)*unitcube, white, thick(), nolight);
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draw(shift(0,2,0)*unitcube, white, thick(), nolight);
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draw(shift(2,2,0)*unitcube, white, thick(), nolight);
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draw(shift(0,3,0)*unitcube, white, thick(), nolight);
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draw(shift(0,3,1)*unitcube, white, thick(), nolight);
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draw(shift(1,3,0)*unitcube, white, thick(), nolight);
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draw(shift(2,3,0)*unitcube, white, thick(), nolight);
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draw(shift(2,3,1)*unitcube, white, thick(), nolight);
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</asy>
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<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12 </math>
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==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.
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 +
{{AMC8 box|year=2003|num-b=12|num-a=14}}

Revision as of 09:07, 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
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