Coloring Circles
Molly McKee
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Problem: You have three crayons, red, blue, and green, for coloring the circles in the figure.
The rules for coloring the circles are:
1. all circles must be colored
2. not all colors need to be used
3. no circles connected by a single line may be the same color
How many different color patterns are possible?
From rule 1 and rule 2, we know there are no patterns which work with zero or one color.
Let’s examine patterns using only two colors:
3 circles will be colored with the first color and 2 will be colored with the second color
We have 3 choices for the first color and then 2 choices for the second color
(3)(2) = 6
Let’s examine patterns using three colors:
We have 3 choices for the first color, 2 choices for the second color, and 1 choice for the third
(3)(2)(1) = 6
The center circle is different from the other four circles
Three circles are the same color, while the remaining two are different
More patterns
