Quoted from Yoski:

Perfect solution to the problem. See below. I let the algorithm run over the long weekend and it came up with the solution shown below.
Round 1
1 6 8
2 7 12
3 9 11
4 5 10
Round 2
0 10 11
4 7 9
2 3 6
5 8 12
Round 3
4 11 12
8 9 10
1 3 5
0 6 7
Round 4
6 10 12
2 5 9
0 1 4
7 8 11
Round 5
0 3 9
2 8 12
5 6 11
1 7 10
Round 6
1 2 11
0 8 10
3 4 7
6 9 12
Round 7
0 9 12
1 2 10
5 7 11
3 4 8
Round 8
3 10 12
0 2 11
1 8 9
4 5 6
Round 9
0 5 7
2 4 9
1 11 12
3 6 10
Round 10
0 1 6
3 7 12
2 5 8
4 10 11
Round 11
1 7 9
2 4 6
3 8 11
0 5 12
Round 12
0 2 3
6 7 8
1 4 12
5 9 10
Round 13
1 3 5
6 9 11
2 7 10
0 4 8
0 1 2 3 4 5 6 7 8 9 10 11 12
#0. 0 2 2 2 2 2 2 2 2 2 2 2 2
#1. 0 0 2 2 2 2 2 2 2 2 2 2 2
#2. 0 0 0 2 2 2 2 2 2 2 2 2 2
#3. 0 0 0 0 2 2 2 2 2 2 2 2 2
#4. 0 0 0 0 0 2 2 2 2 2 2 2 2
#5. 0 0 0 0 0 0 2 2 2 2 2 2 2
#6. 0 0 0 0 0 0 0 2 2 2 2 2 2
#7. 0 0 0 0 0 0 0 0 2 2 2 2 2
#8. 0 0 0 0 0 0 0 0 0 2 2 2 2
#9. 0 0 0 0 0 0 0 0 0 0 2 2 2
#10. 0 0 0 0 0 0 0 0 0 0 0 2 2
#11. 0 0 0 0 0 0 0 0 0 0 0 0 2
#12. 0 0 0 0 0 0 0 0 0 0 0 0 0