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? |
| + | |||
==Solution== | ==Solution== | ||
| − | The cube is | + | The cube is <math>4\times 4\times4</math>. Only the inside sub-cubes are unpainted, thus <math>8</math> are unpainted, leaving <math>64-8=56</math> painted. |
==See also== | ==See also== | ||
| − | + | {{ARML box|year=2005|state=Alabama|num-b=1|num-a=3}} | |
| − | + | ||
| − | + | [[Category:Intermediate Combinatorics Problems]] | |
Latest revision as of 12:06, 26 January 2009
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 
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 | ||
