Mário built a cube with twelve equal sticks and wants to paint them so that no vertex has sticks of the same color meeting there. What is the minimum number of colors he needs to use?
A) 2
B) 3
C) 4
D) 6
E) 8
Solution

## ALTERNATIVE B

Each vertex is the endpoint of three edges and, therefore, at least three different colors are needed. On the other hand, three different colors are enough; we can see this in the figure, where three different colors are indicated by solid, dashed, and dotted lines.

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-34.jpg?height=202&width=235&top_left_y=1658&top_left_x=1019)

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