I think it would be nice to have a place to compile all the ideas for different game modes that people have here in the comments.
survival: timer for someone to see how many puzzles they can solve in a period of time, play for personal best.
races for 2 or more people to compete who can solve puzzles the fastest
duel: a ranking system where 2 people would play the same difficult puzzle and see who can solve it without caring about time. Each person gets 6 hours to solve the puzzle. Won’t work without a difficulty rating system in place, might want a trophy system too.
arcade?? imagine matching shapes like the google halloween cat game, except instead of drawing shapes youre folding them
Mini achievements that are focused on things like variety, perseverance, difficulty…anything other than speed. I play in the evenings to wind-down, not UP