Hi my name is Krystina Fernandez
The level of my question is middle(6-9)
and I am a student.

I was wondering if you knew the answer to this question, Luanne was making party favors for her little sister's birthday party. Each party favor was in the shape of a cube. Luanne had pink and purple paint to paint the cubes and she could paint each face only solid pink or solid purple (no dots,stripes,ect.).For example, one cube may be all purple, another may have two purple faces and four pink faces. Her little sister wanted to have a different cube for each guest.(A cube is not considered different if it can be turned so that all it's sides match the corresponding sides of another cube.)How many different cubes was it possible for Luanne to make?


Hi Krystina

All pink: One way
5 pink, 1 purple: One way
4 pink, 2 purple: Two ways (purple sides opposite or adjacent)
3 pink, 3 purple: Two ways (depending on whether there are two opposite purple sides or not)
2 pink, 4 purple: Two ways
1 pink, 5 purple: One way
All purple: One way.

In all, 10 ways.

To spice up the problem, you could use 3 colours instead of two. One modern branch of mathematics called "P\'olya's theory of enumeration" deals with this kind of painting of cubes.

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