WARNING FOR RIDDLE ANSWER ATTEMPT
I’m pretty sure this works, but I’m tired so I may have missed something. It also doesn’t seem like the most efficient solution, which is worrying.
-Scale 1—————Scale 2———-Aside
1,2,3,4,5,———–7,8,9,10,12——6,11,13
1,3,7,9,11———–2,4,6,8,10——–5,12,13
1,2,7,8—————3,4,9,10———–13
This should result in the following mapping, where L: left side is light, R: right side is light, and B: the two are perfectly balanced (as all things should be).
1 LLL
2 LRL
3 LLR
4 LRR
5 LBB
6 BRB
7 RLL
8 RRL
9 RLR
10 RRR
11 BLB
12 RBB
13 BBB