The center of mass of the entire system lies at the intersection of the three twigs, which is directly below the top acorn. This is why the configuration of three acorns stays balanced upright.
Yes, the configuration of three acorns stays balanced upright. This is because the center of mass of the system lies directly below the point where the stick supports the top acorn. The center of mass is the point at which the weight of the entire system seems to be concentrated. If the center of mass is directly below the support point, then the torque on the system is zero and it will not topple.
In the case of the three acorns, the center of mass is located at the intersection of the three twigs. This point is directly below the top acorn, so the system is balanced.
To see why the center of mass is located at the intersection of the three twigs, consider the following. Each twig exerts a force on the acorn it is connected to. This force is equal to the weight of the acorn divided by the length of the twig. The direction of the force is along the length of the twig.
The three forces acting on the top acorn are coplanar and concurrent, which means they lie in the same plane and intersect at a single point. This point is the center of mass of the system.
The same reasoning can be applied to the two lower acorns. The forces acting on each acorn are coplanar and concurrent, and the center of mass of each acorn is located at the intersection of the two twigs that connect it to the other acorns.
Therefore, the center of mass of the entire system lies at the intersection of the three twigs, which is directly below the top acorn. This is why the configuration of three acorns stays balanced upright.