Sometimes the efforts of many add neatly, as when many arms try to lift a gate.
Other times, they add imperfectly, as when many eyes try to sight or many ears to hear. It's a mix of varying factors: what's being sensed "out there" and the individual's attention. The individual can only contribute so much.
Other times, additional hands are useless, as when picking a lock, or downright counterproductive, as when many people try to hide or sneak.
In a game, very few skills add neatly except for the sheer application of brute force. Those that add uselessly should be obvious. Which leaves the imperfect and the counterproductive situations to deal with.
So when adding skills imperfectly (and why not, there are diminishing returns even when opening a door because only so many people can get good leverage):
One person = one check
2-3 people = 2 checks
4-7 people = 3 checks, made by the 3 best people
8-15 = 4 checks, made by the 4 best, and so on.
Each power of 2 adds another check.
And when skills interfere - as when a large group is trying to sneak:
One person =one check
2 people = 2 checks
Up to 4 people = 3 checks, made by the 3 worst people
Up to 8 = 4 checks, made by the 4 worst, and so on.
Up to 16 = 5 checks and so on.
Failure by any one means noise is made or they can be seen.
On Abstraction and Saving Throws
40 minutes ago