A friend of ours has gifted us a different sort of boardgame. Time Stories is a puzzle-type game that will take multiple plays to solve. Once solved, it's not really playable again so you either need a fresh 'mystery' deck of cards or to gift the game on (hence the original gifting).
The theme is of time travellers venturing back (in this case) in time to resolve some past mystery. You have a very limited number of moves in which to complete the task. If you don't, the game ends and you start from scratch on the next play - except that you now have some memory of which things were successful and which were, um, disastrous.
Thus, gradually you build up enough knowledge to progress smoothly through the earlier phases and hopefully get to the end; especially if you play consistently with the same set of players - which makes it a great social occasion too.
Not our usual style of game but an interesting change and I'm looking forward to our next attempt.