Coloring Circles

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 segment may be the same color.

How many different color patterns are possible?
   Here are some examples.


     Click HERE to see a page of many of the patterns, ready to color . . .

Is that useful?    


Is this a "good" problem?   What mathematics is involved?  What problem solving strategies?    Is there a simpler solution than what you have pursued?


How is the problem or its solution changed by adding a segment connecting the lower two circles?

Reference: Northeast Georgia RESA Mathematics Tournament, January 1989.

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