SOLUTION: The forty-eight faces of eight unit cubes are painted white. What is the smallest number of these faces that can be repainted black so that it becomes impossible to arrange the cu

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The forty-eight faces of eight unit cubes are painted white. What is the smallest number of these faces that can be repainted black so that it becomes impossible to arrange the cu      Log On


   

Question 67498: The forty-eight faces of eight unit cubes are painted white. What is the smallest number of these faces that can be repainted black so that it becomes impossible to arrange the cubes into a 2x2x2 cube, each of whose six faces is totally white?
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
When the unit cubes are arranged into a single larger cube there will be 24 exposed faces and 24 hidden faces. Each of the unit cubes will have 3 faces exposed so as soon as four faces on a single unit cube have been painted black then one exposed face must be black.
The largest number of faces that can be painted black and still show no exposed black would be if the 24 hidden faces were all black.