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.