I did find that solution for 4-2 when going as far back as possible to get to 6-3, but after trying to use that solution just for 5-1, I thought, "wow, this is useless, let me go back and use the normal solution." But it is actually possible to solve everything in 5 and 6 with that??
I was happy to just get the straightforward solution for 6-3, without having to keep all the contingent paths in my head… but I guess that's what makes the challenge!
Can you confirm, what the first stage with multiple solutions is? Does everything before 4-2 only have one solution? (4-2 is the first stage where I found more than one)
oh yes I did see that trivial alternative for 3-1, I meant nontrivial multiple solutions, but you got that :). Thank you for confirming!
Out of curiosity, do you have a backend system for verifying solvability and solutions? If so, is it brute force, or something more elegant, even heuristics that cut down on the size of the possible solution space?
I do not have an automated solution. I do however have a couple of theories that checkout:
I know that in order to get a solution with crossed lines, you need at lest one tile with crossed lines.
I also know that a set of tiles can solve any puzzle if every line can reach every position (assuming the size of the puzzle is big enough). That's also why I slowly increase the puzzle size as the puzzles get more complicated.