Difference between revisions of "2005 Alabama ARML TST Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | A large cube is painted green and then chopped up into 64 smaller congruent cubes. How many of the smaller cubes have at least one face painted green? | + | A large [[cube (geometry) | cube]] is painted green and then chopped up into 64 smaller congruent cubes. How many of the smaller cubes have at least one face painted green? |
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==Solution== | ==Solution== | ||
The cube is 4x4x4. Only the inside subcubes are unpainted, thus all but 8 are unpainted, leaving 64-8=56 painted. | The cube is 4x4x4. Only the inside subcubes are unpainted, thus all but 8 are unpainted, leaving 64-8=56 painted. | ||
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==See also== | ==See also== | ||
*[[2005 Alabama ARML TST]] | *[[2005 Alabama ARML TST]] | ||
| − | *[[2005 Alabama ARML TST/Problem 1 | Previous Problem]] | + | *[[2005 Alabama ARML TST Problems/Problem 1 | Previous Problem]] |
| − | *[[2005 Alabama ARML TST/Problem 3 | Next Problem]] | + | *[[2005 Alabama ARML TST Problems/Problem 3 | Next Problem]] |
Revision as of 17:21, 17 November 2006
Problem
A large cube is painted green and then chopped up into 64 smaller congruent cubes. How many of the smaller cubes have at least one face painted green?
Solution
The cube is 4x4x4. Only the inside subcubes are unpainted, thus all but 8 are unpainted, leaving 64-8=56 painted.
