# Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 15"

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== Problem == | == Problem == | ||

− | A <math> | + | 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 cube is composed of unit cubes. The faces of unit cubes are colored red. An arrangement of the cubes is "intriguing" if there is exactly red unit cube in every rectangular box composed of unit cubes. Determine the number of "intriguing" colorings.

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*