A question specifies two identical conducting spheres, both of negligible radius (I take this to mean they're to be treated as point charges), and with charges of opposite sign. They're separated by some distance, and the force with which they attract each other is also provided.
They are now connected by a conducting wire, and the force with which they repel each other at equilibrium is also provided. We're required to find the initial charges on the spheres.
The solution treats the final charges on both spheres to be the average of the initial charges on them.
How do you get there? The usual calculations of equating potentials to find the final situation can't be done here, since they're point charges. I don't really see how you can calculate the charges flowing from and to point objects, since charge, as I understand it, is defined to be a point entity itself.