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Eleanor is going to color the sides of a regular octagon. Two sides will be red, two sides will be yellow, two sides will be green, and two sides will be blue. Furthermore, opposite sides of the regular octagon will have the same color. How many different ways can Eleanor color the sides of the ocatgon? (Two patterns are considered identical if one can be rotated to form the other.)

 

 

Would there be 4 different sets of a same color side? If so, would there be 4! ways??

Thanks.

 Dec 22, 2019
 #1
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There are 4 ways to color the red sides, then three ways to color the yellow sides, then two ways to color the green sides, then o one way to color the blue sides.  Answer = 4*3*2*1 = 24.

 Dec 22, 2019
 #2
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That's wrong though...

Guest Dec 22, 2019
 #3
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After you get 24, you have to divide by 8 for the rotation.  So the number is 24/8 = 3.

Guest Dec 22, 2019
 #4
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Nvm, I tried it again and got 6, which is correct.

 

Thanks for the help though!

Guest Dec 22, 2019

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