Number of Possible Combinations for this Hexagon [closed]

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Given the following:



  • a hexagon, which has 6 "spokes" radiating outward from its center toward the corners

  • 3 different crayons (markers, pencils, etc)

How many ways can I color one, two, or three of the "spokes" of the hexagon, not including combinations that are rotations of another combination? What process did you use to determine the answer?




combinations word-problem




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closed as off-topic by amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did Aug 29 at 8:43


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up vote
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down vote

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Given the following:



  • a hexagon, which has 6 "spokes" radiating outward from its center toward the corners

  • 3 different crayons (markers, pencils, etc)

How many ways can I color one, two, or three of the "spokes" of the hexagon, not including combinations that are rotations of another combination? What process did you use to determine the answer?




combinations word-problem




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closed as off-topic by amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did Aug 29 at 8:43


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    you are likely to get answers or help on your question if you show your effort or share your thoughts about the problem
    – Deepesh Meena
    Aug 25 at 2:37










  • I can't have images, since I don't have 10 rep, so...
    – The Eye
    Aug 25 at 2:45










  • You may post a link to an image.
    – N. F. Taussig
    Aug 25 at 7:49










  • I have now done so.
    – The Eye
    Aug 28 at 0:38










  • Please read the how-to-ask page, which was shown to you on the ask-a-question page.
    – user21820
    Aug 29 at 4:03












up vote
-2
down vote

favorite
1









up vote
-2
down vote

favorite
1






1





Given the following:



  • a hexagon, which has 6 "spokes" radiating outward from its center toward the corners

  • 3 different crayons (markers, pencils, etc)

How many ways can I color one, two, or three of the "spokes" of the hexagon, not including combinations that are rotations of another combination? What process did you use to determine the answer?




combinations word-problem




share|cite|improve this question














Given the following:



  • a hexagon, which has 6 "spokes" radiating outward from its center toward the corners

  • 3 different crayons (markers, pencils, etc)

How many ways can I color one, two, or three of the "spokes" of the hexagon, not including combinations that are rotations of another combination? What process did you use to determine the answer?





combinations word-problem





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edited Aug 28 at 22:56









Mike Pierce

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asked Aug 25 at 2:14









The Eye

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closed as off-topic by amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did Aug 29 at 8:43


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did Aug 29 at 8:43


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Jendrik Stelzner, Xander Henderson, user21820, Did
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 2




    you are likely to get answers or help on your question if you show your effort or share your thoughts about the problem
    – Deepesh Meena
    Aug 25 at 2:37










  • I can't have images, since I don't have 10 rep, so...
    – The Eye
    Aug 25 at 2:45










  • You may post a link to an image.
    – N. F. Taussig
    Aug 25 at 7:49










  • I have now done so.
    – The Eye
    Aug 28 at 0:38










  • Please read the how-to-ask page, which was shown to you on the ask-a-question page.
    – user21820
    Aug 29 at 4:03












  • 2




    you are likely to get answers or help on your question if you show your effort or share your thoughts about the problem
    – Deepesh Meena
    Aug 25 at 2:37










  • I can't have images, since I don't have 10 rep, so...
    – The Eye
    Aug 25 at 2:45










  • You may post a link to an image.
    – N. F. Taussig
    Aug 25 at 7:49










  • I have now done so.
    – The Eye
    Aug 28 at 0:38










  • Please read the how-to-ask page, which was shown to you on the ask-a-question page.
    – user21820
    Aug 29 at 4:03







2




2




you are likely to get answers or help on your question if you show your effort or share your thoughts about the problem
– Deepesh Meena
Aug 25 at 2:37




you are likely to get answers or help on your question if you show your effort or share your thoughts about the problem
– Deepesh Meena
Aug 25 at 2:37












I can't have images, since I don't have 10 rep, so...
– The Eye
Aug 25 at 2:45




I can't have images, since I don't have 10 rep, so...
– The Eye
Aug 25 at 2:45












You may post a link to an image.
– N. F. Taussig
Aug 25 at 7:49




You may post a link to an image.
– N. F. Taussig
Aug 25 at 7:49












I have now done so.
– The Eye
Aug 28 at 0:38




I have now done so.
– The Eye
Aug 28 at 0:38












Please read the how-to-ask page, which was shown to you on the ask-a-question page.
– user21820
Aug 29 at 4:03




Please read the how-to-ask page, which was shown to you on the ask-a-question page.
– user21820
Aug 29 at 4:03










1 Answer
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For one spoke there are only three ways, because you might as well color the spoke pointing up. For two spokes, color the spoke pointing up in one of three ways, then choose the other spoke to color in five ways and choose its color in three ways for $45$. All but three of them have been counted twice-the three which have not are the ones with opposite spokes the same color. The number is then $3+frac 12(45-3)=24$. The same idea works for coloring three spokes. I leave that to you.






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    1 Answer
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    1 Answer
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    active

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    active

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    active

    oldest

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    up vote
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    down vote













    For one spoke there are only three ways, because you might as well color the spoke pointing up. For two spokes, color the spoke pointing up in one of three ways, then choose the other spoke to color in five ways and choose its color in three ways for $45$. All but three of them have been counted twice-the three which have not are the ones with opposite spokes the same color. The number is then $3+frac 12(45-3)=24$. The same idea works for coloring three spokes. I leave that to you.






    share|cite|improve this answer
























      up vote
      0
      down vote













      For one spoke there are only three ways, because you might as well color the spoke pointing up. For two spokes, color the spoke pointing up in one of three ways, then choose the other spoke to color in five ways and choose its color in three ways for $45$. All but three of them have been counted twice-the three which have not are the ones with opposite spokes the same color. The number is then $3+frac 12(45-3)=24$. The same idea works for coloring three spokes. I leave that to you.






      share|cite|improve this answer






















        up vote
        0
        down vote










        up vote
        0
        down vote









        For one spoke there are only three ways, because you might as well color the spoke pointing up. For two spokes, color the spoke pointing up in one of three ways, then choose the other spoke to color in five ways and choose its color in three ways for $45$. All but three of them have been counted twice-the three which have not are the ones with opposite spokes the same color. The number is then $3+frac 12(45-3)=24$. The same idea works for coloring three spokes. I leave that to you.






        share|cite|improve this answer












        For one spoke there are only three ways, because you might as well color the spoke pointing up. For two spokes, color the spoke pointing up in one of three ways, then choose the other spoke to color in five ways and choose its color in three ways for $45$. All but three of them have been counted twice-the three which have not are the ones with opposite spokes the same color. The number is then $3+frac 12(45-3)=24$. The same idea works for coloring three spokes. I leave that to you.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 28 at 0:49









        Ross Millikan

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