Imagine a length of rope whose cross section is a regular polygon. You join the ends together with a powerful glue, but before doing so you give one end a twist so that faces are matched up with different faces. Now color each face a different color. How many colors are needed to color the rope? (Mason et al, Thinking Mathematically (Addison-Wesley, 1985), p. 112.
Try special case: 2-dimensional strip to make Mobius strip with only one color needed.
Experiment with lots of different shapes, looking for patterns.
Don't give up! Develop method of recording data systematically. Use physical objects to help.
Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!
Last updated 30 November, 2004