# Charge distribution for three connected conductor spheres

In the auxiliary material of the physics textbook of Halliday, first chapter about electrostatics, there is an example that has the following statement and solution:

basically there are three identical conducting spheres. One has a charge $$Q$$, the others have no charge. The spheres are away from each other. They are now connected by two thin conducting wires (one from sphere 1 to sphere 2. The other from sphere 2 to sphere 3). Then the wire from 2 to 3 is cut, then the wire from 1 to 2 is cut. What is the final charge of sphere 1 ? The surprising answer is $$Q/4$$.

It is surprising because one expects it to be $$Q/3$$ since that is the only way to guarantee that all spheres are at the same potential when they are all connected. But the original answer, $$Q/4$$, seems to suggest that the charge actually separates as much as possible, going to the extremes (sphere 1 and 3, each one with $$Q/2$$, and the center with null charge) and then, when the first wire is cut, the net charge $$Q/2$$ divides among the two still connected spheres. We think is a mistake in the book, because it does not take into account the potential when all spheres are connected, but maybe we are overlooking something. Any guidance for the sake of learning is welcome. Thanks