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 (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.
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A <math>4\times4\times4</math> [[cube (geometry) | cube]] is composed of <math>64</math> unit cubes. The faces of <math>16</math> unit cubes are colored red. An arrangement of the cubes is "intriguing" if there is exactly <math>1</math> red unit cube in every <math>1\times1\times4</math> rectangular box composed of <math>4</math> unit cubes. Determine the number of "intriguing" colorings.
  
 
[[Image:CubeArt.jpg]]
 
[[Image:CubeArt.jpg]]

Revision as of 20:06, 29 January 2009

Problem

A $4\times4\times4$ cube is composed of $64$ unit cubes. The faces of $16$ unit cubes are colored red. An arrangement of the cubes is "intriguing" if there is exactly $1$ red unit cube in every $1\times1\times4$ rectangular box composed of $4$ unit cubes. Determine the number of "intriguing" colorings.

CubeArt.jpg

Solution

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