List combination algorithm

[nuzzle]

You can represent the pairs in a table like this.

   1   2   3   4
1      x   x   x
2          x   x
3              x
4

For example the upper left x represents the 1,2 pair.

Now the problems is to visit the x in a sequence that obeys the non-repetition rule. For example you did it like this,

   1   2   3   4
1      1   5   4
2          2   6
3              3
4

I claim (without proof) that there's a systematic visiting order that always obeys the rule. This is when you move diagonally back and forth along ever smaller diagonals like (I put in an extra number to make the system more visible),

   1   2   3   4  5
1      1   7   8  10
2          2   6  9
3              3  5
4                 4
5

And this is the corresponding list,

1,2
2,3
3,4
4,5
3,5
2,4
1,3
1.4
2,5
1,5