Math nerdy help needed on a creative project

[sunrain]

Hello hello.

I need a list that shows all the ways that the numbers 1-6 can combine between themselves and with another group of the same set of numbers. Order does not matter and (this is what I assume is the tricky part) only groups of (2,3,4, and 5) numbers should be considered. I have no idea how to calculate this and I figured it was probably trivial for the math whizzes around here.

[tomoe]

Is this with or without replacement? i.e. can you have 11, 22, 33, etc.?

[sunrain]

Excellent question I didn't think of. I wouldn't want that.

[Lucid]

I'm not quite sure that I understood your problem correctly, but I think you're asking for every combination of numbers in the set {1, 2, 3, 4, 5, 6} of lengths 2 through 5, without repeats. If I'm right, then this should be the list, which I wrote a simple program to generate (and you could also do this by hand fairly quickly). If you want to see the code, which I highly doubt you do, I can post it later.

Length 2:
1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
4 5
4 6
5 6

Length 3:
1 2 3
1 2 4
1 2 5
1 2 6
1 3 4
1 3 5
1 3 6
1 4 5
1 4 6
1 5 6
2 3 4
2 3 5
2 3 6
2 4 5
2 4 6
2 5 6
3 4 5
3 4 6
3 5 6
4 5 6

Length 4:
1 2 3 4
1 2 3 5
1 2 3 6
1 2 4 5
1 2 4 6
1 2 5 6
1 3 4 5
1 3 4 6
1 3 5 6
1 4 5 6
2 3 4 5
2 3 4 6
2 3 5 6
2 4 5 6
3 4 5 6

Length 5:
1 2 3 4 5
1 2 3 4 6
1 2 3 5 6
1 2 4 5 6
1 3 4 5 6
2 3 4 5 6

[sunrain]

Lucid,
Thanks for the reply. That shows all the ways that the numbers 1-6 can combine between themselves of lengths 2-5. For my whole problem to be solved I also need that group of combinations compared in the same way against another group of the same set of numbers. I'm terrible at word problems so I hope I'm phrasing this clearly.

[billybobsky]

what? what do you mean by compared?

[Bryson]

Rather than abstracting it, tell us what you're actually trying to do and we might understand the question better. Right now I'm unclear what you mean - it might make more sense with some context.

[Lucid]

Yeah, I'm having trouble understanding what you want to do with the second set. You stated that you don't want any repeated numbers in the list (like 11, or 11451) so I don't see what the second set would add to the list, seeing as they are the same numbers. A clarification of what the second set signifies would be nice, as well as putting the problem in context as Bryson suggested.