Distinct surfaces of a painted tetrahedron

[AddyW]

Hey, everyone! Can someone help me with this?

If each surface of a regular tetrahedron is painted a different color (red, green, yellow, or blue), and exactly three of the edges of the tetrahedron are painted white, how many spatially distinct patterns can be formed? "Distinct" meaning not able to coincide by rotation.

 

[Deleted member 4993]

Hey, everyone! Can someone help me with this?

If each surface of a regular tetrahedron is painted a different color (red, green, yellow, or blue), and exactly three of the edges of the tetrahedron are painted white, how many spatially distinct patterns can be formed? "Distinct" meaning not able to coincide by rotation.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about the problem.

 

[The Highlander]

Hey, everyone! Can someone help me with this?

If each surface of a regular tetrahedron is painted a different color (red, green, yellow, or blue), and exactly three of the edges of the tetrahedron are painted white, how many spatially distinct patterns can be formed? "Distinct" meaning not able to coincide by rotation.

You could start by drawing nets of the tetrahedron (there are two distinct possibilities there) but I'm at a loss to see what the answer to the question might be without knowing "exactly" which three edges are white (and do the remainder have no colouration?).

It is also unclear (to me at least) what is meant by: "how many spatially distinct patterns can be formed?".

 

[AddyW]

You could start by drawing nets of the tetrahedron (there are two distinct possibilities there) but I'm at a loss to see what the answer to the question might be without knowing "exactly" which three edges are white (and do the remainder have no colouration?).

It is also unclear (to me at least) what is meant by: "how many spatially distinct patterns can be formed?".

Any of the three edges can be white - so every possibility has to be found including all of the different combinations of white edges. The non-white edges have no coloration. What is the net of the tetrahedron, just its sides laid flat?

 

[AddyW]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

You have posted many problems here without showing a line of original work.

That's just it, I have no clue how to approach this at all. I don't know how to figure out how many color combinations there can be and how many combinations that can be distinct on the sides of a tetrahedron.

 

[The Highlander]

That's just it, I have no clue how to approach this at all. I don't know how to figure out how many color combinations there can be and how many combinations that can be distinct on the sides of a tetrahedron.

So, like I suggested, draw the net(s). Then have a think about how to colour them in. It may be useful just to assign each colour a letter/number rather than actually using coloured pens/pencils?
(Your own 'definition' of a net is pretty much all there is to say about them but, if you feel you need further information, just Google "tetrahedron"; a little bit of effort on your part will go a long way to producing helpful responses from members. We don't do all the work for you in here but are happy to offer suggestions/advice when we can see, from what you submit, exactly where you are struggling. )

Also, has an "answer" been provided with the question?
(It often helps if it's possible to work 'backwards', from the "answer", to confirm the right approach is being adopted.)

 

[AddyW]

So, like I suggested, draw the net(s). Then have a think about how to colour them in. It may be useful just to assign each colour a letter/number rather than actually using coloured pens/pencils?
(Your own 'definition' of a net is pretty much all there is to say about them but, if you feel you need further information, just Google "tetrahedron"; a little bit of effort on your part will go a long way to producing helpful responses from members. We don't do all the work for you in here but are happy to offer suggestions/advice when we can see, from what you submit, exactly where you are struggling. )

Also, has an "answer" been provided with the question?
(It often helps if it's possible to work 'backwards', from the "answer", to confirm the right approach is being adopted.)

I actually figured it out thanks to your help! The answer is just 2. One is a mirror image of the other! In every other way you can paint a tetrahedron it isn't distinct (can be rotated to look like another color combo).