This is the problem given in Purcell and Morin's electricity and magnetism book. (Problem 3.2 If you have the book)
Figure:
I was able to figure out that the charges on A,B,C,D cant be held after connecting C and D because if you consider a loop from A to C and back to A through the wires, for a static electric field, from Kirchhoff's loop rule, $$\oint \vec{E}\cdot d\vec{l}=0$$
If the wires have no resistance, then the potential drops across A-C and B-D will add up and wont be zero. So the charges will disappear as soon as C and D are connected so as to make $\oint \vec{E}\cdot d\vec{l}=0$
But in what way will they cancel out? And I was not able to understand this (stated in the solution):
Won't induced charges have equal magnitude?