I am the guy who did the third puzzle (XD sry if you got an unsolvable third puzzle), and yeah it's randomly generated and I just realized that you got a 50% of chance to have a solvable puzzle and another half unsolvable. (if luck is considered a factor to win the game, it's not a bad mechanism :P)
Not sure if I can still update it since we already submit the game, it going to be just one line of code to make it have fixed order that is solvable.