Difference between revisions of "2005 Alabama ARML TST Problems/Problem 2"
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==Solution== | ==Solution== | ||
| − | The cube is <math>4\times 4\times4</math>. Only the inside sub-cubes are unpainted, thus all but <math>8</math> are unpainted, leaving <math>64-8=56 </math>painted. | + | The cube is <math>4\times 4\times4</math>. Only the inside sub-cubes are unpainted, thus all but <math>8</math> are unpainted, leaving <math>64-8=56</math> painted. |
==See also== | ==See also== | ||
Revision as of 09:07, 19 April 2008
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 
. Only the inside sub-cubes are unpainted, thus all but 
are unpainted, leaving 
painted.
See also
| 2005 Alabama ARML TST (Problems) | ||
| Preceded by: Problem 1 |
Followed by: Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
