Color the cubes, then assemble them to form a larger cube












5














Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a 3x3x3 cube all in yellow, and a 3x3x3 cube all in blue by rearranging the painted cubes, not repainting them.






geometry three-dimensional







share|improve this question









New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
    – Frpzzd
    5 hours ago








  • 1




    You must be able to assemble the cube in each of the colors.
    – Daniel Mathias
    5 hours ago










  • Oh, I see. Thanks for clarifying!
    – Frpzzd
    5 hours ago






  • 1




    I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
    – Bass
    3 hours ago
















5














Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a 3x3x3 cube all in yellow, and a 3x3x3 cube all in blue by rearranging the painted cubes, not repainting them.






geometry three-dimensional







share|improve this question









New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
    – Frpzzd
    5 hours ago








  • 1




    You must be able to assemble the cube in each of the colors.
    – Daniel Mathias
    5 hours ago










  • Oh, I see. Thanks for clarifying!
    – Frpzzd
    5 hours ago






  • 1




    I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
    – Bass
    3 hours ago














5












5








5







Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a 3x3x3 cube all in yellow, and a 3x3x3 cube all in blue by rearranging the painted cubes, not repainting them.






geometry three-dimensional







share|improve this question









New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a 3x3x3 cube all in yellow, and a 3x3x3 cube all in blue by rearranging the painted cubes, not repainting them.






geometry three-dimensional




geometry three-dimensional






share|improve this question









New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 2 hours ago









Brandon_J

487




487






New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 5 hours ago









Daniel Mathias

261




261




New contributor




Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Daniel Mathias is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
    – Frpzzd
    5 hours ago








  • 1




    You must be able to assemble the cube in each of the colors.
    – Daniel Mathias
    5 hours ago










  • Oh, I see. Thanks for clarifying!
    – Frpzzd
    5 hours ago






  • 1




    I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
    – Bass
    3 hours ago


















  • Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
    – Frpzzd
    5 hours ago








  • 1




    You must be able to assemble the cube in each of the colors.
    – Daniel Mathias
    5 hours ago










  • Oh, I see. Thanks for clarifying!
    – Frpzzd
    5 hours ago






  • 1




    I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
    – Bass
    3 hours ago
















Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
– Frpzzd
5 hours ago






Welcome to PSE! Your question seems unclear to me. Why not just put the cubes into a 3x3x3 cube shape, paint the faces of the larger cube, disassemble, and then paint the rest of the faces whatever colors we want?
– Frpzzd
5 hours ago






1




1




You must be able to assemble the cube in each of the colors.
– Daniel Mathias
5 hours ago




You must be able to assemble the cube in each of the colors.
– Daniel Mathias
5 hours ago












Oh, I see. Thanks for clarifying!
– Frpzzd
5 hours ago




Oh, I see. Thanks for clarifying!
– Frpzzd
5 hours ago




1




1




I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
– Bass
3 hours ago




I ran into the same problem as @Frpzzd, so I tried to edit the question to be a bit more difficult to misunderstand. My sentence structure still seems a bit convoluted, so please feel free to improve it however you see fit.
– Bass
3 hours ago










2 Answers
2






active

oldest

votes


















5














Paint the small cubes with the colors red, blue, and green as follows, so that on each cube, the faces with the same color are all mutually adjacent.




  • One cube with three red faces and three blue faces

  • One cube with three red faces and three green faces

  • One cube with three blue faces and three green faces

  • Three cubes each with three red faces, two blue faces, and one green face

  • Three cubes each with three red faces, two green faces, and one blue face

  • Three cubes each with three blue faces, two red faces, and one green face

  • Three cubes each with three blue faces, two green faces, and one red face

  • Three cubes each with three green faces, two red faces, and one blue face

  • Three cubes each with three green faces, two blue faces, and one red face

  • Six cubes with two faces of each color


Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.






share|improve this answer





















  • Much better than my answer; well done!
    – Hugh
    4 hours ago










  • @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
    – Frpzzd
    4 hours ago










  • Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
    – Hugh
    3 hours ago






  • 2




    This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
    – JonMark Perry
    2 hours ago










  • @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
    – Hugh
    49 mins ago



















0














This sounds very similar to...




this puzzle featured in a video by TED-ED. I'll try and make a picture when I get home.







share|improve this answer





















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    2 Answers
    2






    active

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    2 Answers
    2






    active

    oldest

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    active

    oldest

    votes






    active

    oldest

    votes









    5














    Paint the small cubes with the colors red, blue, and green as follows, so that on each cube, the faces with the same color are all mutually adjacent.




    • One cube with three red faces and three blue faces

    • One cube with three red faces and three green faces

    • One cube with three blue faces and three green faces

    • Three cubes each with three red faces, two blue faces, and one green face

    • Three cubes each with three red faces, two green faces, and one blue face

    • Three cubes each with three blue faces, two red faces, and one green face

    • Three cubes each with three blue faces, two green faces, and one red face

    • Three cubes each with three green faces, two red faces, and one blue face

    • Three cubes each with three green faces, two blue faces, and one red face

    • Six cubes with two faces of each color


    Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.






    share|improve this answer





















    • Much better than my answer; well done!
      – Hugh
      4 hours ago










    • @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
      – Frpzzd
      4 hours ago










    • Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
      – Hugh
      3 hours ago






    • 2




      This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
      – JonMark Perry
      2 hours ago










    • @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
      – Hugh
      49 mins ago
















    5














    Paint the small cubes with the colors red, blue, and green as follows, so that on each cube, the faces with the same color are all mutually adjacent.




    • One cube with three red faces and three blue faces

    • One cube with three red faces and three green faces

    • One cube with three blue faces and three green faces

    • Three cubes each with three red faces, two blue faces, and one green face

    • Three cubes each with three red faces, two green faces, and one blue face

    • Three cubes each with three blue faces, two red faces, and one green face

    • Three cubes each with three blue faces, two green faces, and one red face

    • Three cubes each with three green faces, two red faces, and one blue face

    • Three cubes each with three green faces, two blue faces, and one red face

    • Six cubes with two faces of each color


    Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.






    share|improve this answer





















    • Much better than my answer; well done!
      – Hugh
      4 hours ago










    • @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
      – Frpzzd
      4 hours ago










    • Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
      – Hugh
      3 hours ago






    • 2




      This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
      – JonMark Perry
      2 hours ago










    • @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
      – Hugh
      49 mins ago














    5












    5








    5






    Paint the small cubes with the colors red, blue, and green as follows, so that on each cube, the faces with the same color are all mutually adjacent.




    • One cube with three red faces and three blue faces

    • One cube with three red faces and three green faces

    • One cube with three blue faces and three green faces

    • Three cubes each with three red faces, two blue faces, and one green face

    • Three cubes each with three red faces, two green faces, and one blue face

    • Three cubes each with three blue faces, two red faces, and one green face

    • Three cubes each with three blue faces, two green faces, and one red face

    • Three cubes each with three green faces, two red faces, and one blue face

    • Three cubes each with three green faces, two blue faces, and one red face

    • Six cubes with two faces of each color


    Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.






    share|improve this answer












    Paint the small cubes with the colors red, blue, and green as follows, so that on each cube, the faces with the same color are all mutually adjacent.




    • One cube with three red faces and three blue faces

    • One cube with three red faces and three green faces

    • One cube with three blue faces and three green faces

    • Three cubes each with three red faces, two blue faces, and one green face

    • Three cubes each with three red faces, two green faces, and one blue face

    • Three cubes each with three blue faces, two red faces, and one green face

    • Three cubes each with three blue faces, two green faces, and one red face

    • Three cubes each with three green faces, two red faces, and one blue face

    • Three cubes each with three green faces, two blue faces, and one red face

    • Six cubes with two faces of each color


    Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.







    share|improve this answer












    share|improve this answer



    share|improve this answer










    answered 4 hours ago









    Frpzzd

    652119




    652119












    • Much better than my answer; well done!
      – Hugh
      4 hours ago










    • @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
      – Frpzzd
      4 hours ago










    • Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
      – Hugh
      3 hours ago






    • 2




      This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
      – JonMark Perry
      2 hours ago










    • @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
      – Hugh
      49 mins ago


















    • Much better than my answer; well done!
      – Hugh
      4 hours ago










    • @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
      – Frpzzd
      4 hours ago










    • Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
      – Hugh
      3 hours ago






    • 2




      This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
      – JonMark Perry
      2 hours ago










    • @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
      – Hugh
      49 mins ago
















    Much better than my answer; well done!
    – Hugh
    4 hours ago




    Much better than my answer; well done!
    – Hugh
    4 hours ago












    @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
    – Frpzzd
    4 hours ago




    @Hugh Thanks! It would be nice to generalize it. The 4x4x4 cube with 3 colors is pretty much trivial, but with 4 colors... hmm...
    – Frpzzd
    4 hours ago












    Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
    – Hugh
    3 hours ago




    Oh, that's a good puzzle... A 4*4*4 with 3 colours can't be too difficult, but with 4 colours it could get tough. I'm pretty sure it could be done though! You know what I'll be working on ;)
    – Hugh
    3 hours ago




    2




    2




    This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
    – JonMark Perry
    2 hours ago




    This looks very like the expansion of $(RG+GB+BR)^3$ - I haven't figured out quite how yet though!
    – JonMark Perry
    2 hours ago












    @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
    – Hugh
    49 mins ago




    @JonMarkPerry oh, nice observation. That could be a potential lead to follow.
    – Hugh
    49 mins ago











    0














    This sounds very similar to...




    this puzzle featured in a video by TED-ED. I'll try and make a picture when I get home.







    share|improve this answer


























      0














      This sounds very similar to...




      this puzzle featured in a video by TED-ED. I'll try and make a picture when I get home.







      share|improve this answer
























        0












        0








        0






        This sounds very similar to...




        this puzzle featured in a video by TED-ED. I'll try and make a picture when I get home.







        share|improve this answer












        This sounds very similar to...




        this puzzle featured in a video by TED-ED. I'll try and make a picture when I get home.








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        Hugh

        1,3511617




        1,3511617






















            Daniel Mathias is a new contributor. Be nice, and check out our Code of Conduct.










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