The snakes idea is great
By the way, I loved microgue
Here are some ideas:
1) You could have a hub room with several doors. Each door go to another rooms.
The twist is that the same door can lead to different rooms.
The puzzle will be finding the correct exploration order.
Clues could be given by symbols on the walls or colors or notes.
2) The classic colored keys puzzle. The keys could be gems or statues.
3) The exit could be shown on the first room but impossible to reach.
You could have some mirrors that flips the level or change gravity in order to get to the exit
Regarding the match 3; if I understand correctly the question: you have 3 elements(n) that you can combine by 3(m) ?
In this case you have n! / (n-m)! = 3! - (3-3)! = 3*2 - 0 = 6