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 '''''Intriguing''''' 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 '''''Intriguing''''' colorings.
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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.
  
 
== Problem Source ==
 
== Problem Source ==
 
4everwise did not write this problem. The souce cannot be revealed at this moment, as the contest is still running.
 
4everwise did not write this problem. The souce cannot be revealed at this moment, as the contest is still running.

Revision as of 00:15, 25 July 2006

Problem

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

Problem Source

4everwise did not write this problem. The souce cannot be revealed at this moment, as the contest is still running.

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