Color a Circle

Divide a circular region with straight lines, then color the subregions so that adjacent subregions (i.e., those that share a side) are different colors. What is the least number of colors required?

Hints/Solution:Simplify the problem. Does the number of colors depend on the number of dividing lines?

Comments:This problem is a simplification of the famous four-color map problem. In that problem we divide the plane in any aribtrary manner, rather than with straight lines. It has been proved that the least number of colors required in that case is four (though some mathematicians do not accept the "proof" because computers were used). So the answer to the problem posed here is less than or equal to four.

ReflectionIs this a "good" problem? Should it remain in this set? Why? What is the mathematics you have gained from it?

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