Mock AIME 2 2006-2007 Problems/Problem 15: Difference between revisions
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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. | 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: | [[Image:AIME_2006_P15a.png]] | ||
==Solution== | ==Solution== | ||
Revision as of 19:38, 22 November 2023
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
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See Also
| Mock AIME 2 2006-2007 (Problems, Source) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
