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MATH / Fourteen white cubes are put together to form the figure on the right. The…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Fourteen white cubes are put together to form the figure 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]
size(150);
pair a=(1,0),b=(0,1),c=(0.45,0.4);

void drawcube(pair loc){
     filldraw(loc+b--loc--loc+a--loc+a+c--loc+a+b+c--loc+b+c--cycle,white);
     draw(loc+b--loc+a+b--loc+a+b+c^^loc+a+b--loc+a);
}

pair location[]={origin,b,a,2a,3a,3a+b,-c,3a-c,-2c,-2c+b,-2c+a,-2c+2a,-2c+3a,-2c+3a+b};

for(int i; i<14;++i){
   drawcube(location[i]);
}


[/asy]

level

Level 1

type

Counting & Probability

Discussion

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Source and history

task_id
92cd0ab3-be51-56aa-9c35-00a2fbd72eff
task_key
counting~5fand~5fprobability--test--92cd0ab3-be51-56aa-9c35-00a2fbd72eff
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import