Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 15"
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== Problem == | == Problem == | ||
| − | A <math>\displaystyle 4\times4\times4</math> cube is composed of <math>\displaystyle 64</math> unit cubes. The faces of <math>\displaystyle 16</math> unit cubes are colored red. An arrangement of the cubes is <math>\mathfrak{Intriguing}</math> if there is exactly <math>\displaystyle 1</math> red unit cube in every <math>\displaystyle 1\times1\times4</math> rectangular box composed of <math>\displaystyle 4</math> unit cubes. Determine the number of <math>\mathfrak{Intriguing}</math> colorings. | + | A <math>\displaystyle 4\times4\times4</math> [[cube (geometry) | cube]] is composed of <math>\displaystyle 64</math> unit cubes. The faces of <math>\displaystyle 16</math> unit cubes are colored red. An arrangement of the cubes is <math>\mathfrak{Intriguing}</math> if there is exactly <math>\displaystyle 1</math> red unit cube in every <math>\displaystyle 1\times1\times4</math> rectangular box composed of <math>\displaystyle 4</math> unit cubes. Determine the number of <math>\mathfrak{Intriguing}</math> colorings. |
[[Image:CubeArt.jpg]] | [[Image:CubeArt.jpg]] | ||
Revision as of 12:29, 30 October 2006
Problem
A 
cube is composed of 
unit cubes. The faces of 
unit cubes are colored red. An arrangement of the cubes is 
if there is exactly 
red unit cube in every 
rectangular box composed of 
unit cubes. Determine the number of colorings.
Solution
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