Cube Problem
Probability
Level
2
Each face of a cube is painted either white or black. In how many different ways can the cube be painted, (independent of rotation)?
16
10
12
8
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1 solution
1 ) There is one way to paint a cube with 6 white surfaces.
2 ) There is one way to paint a cube with 5 white surfaces and 1 black .
3 ) There are two ways to paint a cube with 4 white surfaces and 2 black : Touching surfaces and opposite surfaces.
4 ) There are two ways to paint a cube with 3 white surfaces and 3 black : All three touching the same corner and a "band" of three surfaces wrapping around the cube.
5 ) 2 white and 4 black is analog to 3 )
6 ) 1 white and 5 black is analog to 2 )
7 ) 6 black is analog to 1 )
1 ) + 2 ) + 3 ) + 4 ) + 5 ) + 6 ) + 7 ) = 1 + 1 + 2 + 2 + 2 + 1 + 1 = 1 0