# eachface of a die is colored with one of only two selected colors.How many different 2 colored dice can be made?

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### 1 Answer

How many different 2 color dice are possible given 2 colors?

Let the two colors be red and blue:

(1) All faces could be red, and this could happen in one way. But this is not two colored.

(2) All the faces could be blue, and this happens in one way. But this also is not two colored.

(3) There could be one red face and five blue faces. This can happen in one way -- all other ways can be rotated to look like this one.

(4) There could be one blue face and five red faces. This happens in one way.

(5) There could be two red faces and four blue faces. This can happen in two ways: The red faces opposite each other, and the red faces adjacent.

(6) As above, there could be two ways to have two blue faces with four red faces.

(6) There are two ways to have 3 red faces and 3 blue faces. The 3 red faces could meet at a vertex (corner), or 2 could be opposite of each other.

Thus there are 1+1+2+2+2=8 2-colored dice.