1. ## Circle of numbers

The numbers 1, 2 and 3 can be formed in 27 different numbers eg 122, 131,111,331,231. how do you place nine 3:s, nine 2:s and nine 1:s in a circle so when read clockwise each number shows exactly once.

By the way is there a better place for this problem in this forum?

2. It's easy enough to come up with such sequences by trial and error, for example

111233121222311333221313232.

But it looks as though you are asking for more than that, like a systematic method for finding such sequences, or maybe an enumeration of all possible answers. I can't help with that.

3. This type of sequence is rather well known and is called de Bruijn Sequence. Unfortunately, I don't think there is an easy way of generating such sequences by hand. But for your case, I think the trick is to just avoid repeating the first two numbers that you started with for as long as you can. For example, if you started with
1231...
Your first two numbers are 1 and 2, so you should avoid putting 2 next because it would repeat the pattern of 12. Pick either 1 or 3 to make it
12311... or 12313...
I can't assure that this always works, but you can test it yourself.

Edit: This really has nothing to do with number theory, so you might consider putting it in a graph theory forum.

4. ## de Bruijn

Yeah, I cheched that guy out. I just canīt make anything out of it, at least to this problem.

I was almost certain that this problem belonged here, but I better replace.

Thanks!