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## Question

You have several white cubes and a jug of red paint. Then you use the red paint to cover one or more sides of each cube. Following such a method, how many distinguishable cubes can you make?

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You have several white cubes and a jug of red paint. Then you use the red paint to cover one or more sides of each cube. Following such a method, how many distinguishable cubes can you make?

It seems like it would depend on how you are allowed to go about doing the distinguishing. To explain ...

1. Single, non-moving vantage point:

Answer: 4, since you can only see three sides of any cube at one time, leaving you with between 0 and 3 red sides.

2. Moving vantage point, without touching cubes, presuming they are resting on a flat surface:

Answer: 6, since you can see five sides of any cube, so you have between 0 and 5 red sides.

3. You can handle the cubes (after the paint has dried, naturally!):

Answer: 7, since there will be between 0 and 6 red sides for each cube.

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You have several white cubes and a jug of red paint. Then you use the red paint to cover one or more sides of each cube. Following such a method, how many distinguishable cubes can you make?
10
0 faces = 1 way

1 face = 1 way

2 faces = 2 ways - adjacent or opposite

3 faces = 2 ways - all touching at a corner or 2 opposite faces and one that connects them

4 faces = 2 ways - reverse of 2

5 faces = 1 way - reverse of 1

6 faces = 1 way.

Nice one.

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10
0 faces = 1 way

1 face = 1 way

2 faces = 2 ways - adjacent or opposite

3 faces = 2 ways - all touching at a corner or 2 opposite faces and one that connects them

4 faces = 2 ways - reverse of 2

5 faces = 1 way - reverse of 1

6 faces = 1 way.

Nice one.

Ugh. Why didn't I think about placement of sides? Nice job.

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