About math solution.. I am trying to it by the following way:
Assume a connection between stops A and B. Then connection from B to A exists too. Then, to satisfy the problem's conditions, we have to introduce (2*n-1)*n connections (ordered in such a way that each tram route has 2*n-1 connections). All the connections are distinct.
Next, each tram stop has exactly 2*n-1 connections to other distinct stops. It is always odd integer, so every tram stop must appear exactly once at the beginning of single route, and next time it must appear (2*n-2)/2=n-1 times in the middle of other routes. It is true for all the routes.
So first we should build the following answer matrix if we consider n = 3:
1 x x x x 4
2 x x x x 5
3 x x x x 6

Then I am trying to place other elements to the matrix according to some placement rules from the thoughts above, but I am still unable to come up with a good solution.
Could someone point out, am I going correct in my math thoughts or such approach leads to naive backtracking solution? Thanks!
Sorry I was so verbose :D

Only math solution   acceptable
because this is structure design problem.
I spent a lot of time but was unable to find it.
Solution easy to find in internet with key words
"decomposing complete graph in hamilton paths"
Use diameters and  walk left-rigth- down with respect to them.

Edited by author 14.08.2009 11:02