AMC 8 2003 Problem 13
Source:
July 23, 2011
geometry3D geometry
Problem Statement
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]