To answer this question, our only concern is what happens to the whole group, about whether the balance pole inclines towards the cliff or it doesn't. To fall down or not to fall down, that's the question.
Only their relative weight and position matters, since the leaning of the pole (that's to say, its equilibrium, and the possibility of falling down) is only related to where they place themselves.
So let's simplify things: let's ask each of the groups to stand together at a single point on each plank. The only condition for this point is: the response of the balance board should be exactly the same as before. Since they are three, and if their weight is approximately the same, it would be quite similar if the three of them were in the same point as the one in the middle. So, let's ask them to put themselves that way. Maybe now it's quite clear which one of them are falling down, isn't it?
I guess you can see it clearly now.The key concept we have played with is called center of gravity. This is a point where if all the existing forces were applied in it, the object would move (or stay) exactly in the same way as when the forces are applied in their actual locations: we shouldn't be able to tell the difference. Although it may sound hard, we're quite used to deal intuitively with this center of gravity.
As a rule of thumb, buildings should be designed so that their center of gravity is located in the right place, between the supports, so that the building doesn't wish to fall. They usually are. But sometimes, they just don't seem so. Then, there are two main possibilities: either big dead weights, hidden somewhere; or hidden supports to prevent them from falling. Both tend to be expensive. It's much better (and cheaper!) just to design with this simple concept in mind: center on the center!