I wasn't aware that clicking different things in different orders affected the outcome. I have just been clicking solve every time it comes up and not reading the captions.
I don't think it does.
Here's the relevant part of the (dart2js'd but slightly cleaned-up) code:
https://gist.github.com/CyberShadow/11329584
Edit: I made a full graph of the entire game: https://news.ycombinator.com/item?id=7652770